discrete gauge transformation?

[LuRan]

Hi all,

I know it sounds a little bit stupid, but this problem keeps bothering
me. Are there any discrete gauge transformations? I mean, can I just
transform the phase of some discrete points in the spacetime and keep
the phase of other points fixed. This may be difficult to express in a
mathematical form, but I see no reason from the gauge principle that
these kind of transform should not exist. But all the textbooks and
papers seem assume the gauge transformation should be continue from the
beginning, Any ideas?

--
Have a nice day,
LR

[Ilja Schmelzer]

"LuRan" <hephooey@hotmail.com> schrieb
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?

If the underlying space is continuous, it usually makes not much sense to
consider discontinous gauge fields on it. But you have some internal
boundary things may be different.

Another interesting domain is lattice gauge theory. Here the underlying
space is, essentially, a lattice, and you can have a discrete gauge group.

Ilja

[Ilja Schmelzer]

"LuRan" <hephooey@hotmail.com> schrieb
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?

If the underlying space is continuous, it usually makes not much sense to
consider discontinous gauge fields on it. But you have some internal
boundary things may be different.

Another interesting domain is lattice gauge theory. Here the underlying
space is, essentially, a lattice, and you can have a discrete gauge group.

Ilja

[Ilja Schmelzer]

"LuRan" <hephooey@hotmail.com> schrieb
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?

If the underlying space is continuous, it usually makes not much sense to
consider discontinous gauge fields on it. But you have some internal
boundary things may be different.

Another interesting domain is lattice gauge theory. Here the underlying
space is, essentially, a lattice, and you can have a discrete gauge group.

Ilja

[Ilja Schmelzer]

"LuRan" <hephooey@hotmail.com> schrieb
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?

If the underlying space is continuous, it usually makes not much sense to
consider discontinous gauge fields on it. But you have some internal
boundary things may be different.

Another interesting domain is lattice gauge theory. Here the underlying
space is, essentially, a lattice, and you can have a discrete gauge group.

Ilja

[Ilja Schmelzer]

"LuRan" <hephooey@hotmail.com> schrieb
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?

If the underlying space is continuous, it usually makes not much sense to
consider discontinous gauge fields on it. But you have some internal
boundary things may be different.

Another interesting domain is lattice gauge theory. Here the underlying
space is, essentially, a lattice, and you can have a discrete gauge group.

Ilja

[Ilja Schmelzer]

"LuRan" <hephooey@hotmail.com> schrieb
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?

If the underlying space is continuous, it usually makes not much sense to
consider discontinous gauge fields on it. But you have some internal
boundary things may be different.

Another interesting domain is lattice gauge theory. Here the underlying
space is, essentially, a lattice, and you can have a discrete gauge group.

Ilja

[Ilja Schmelzer]

"LuRan" <hephooey@hotmail.com> schrieb
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?

If the underlying space is continuous, it usually makes not much sense to
consider discontinous gauge fields on it. But you have some internal
boundary things may be different.

Another interesting domain is lattice gauge theory. Here the underlying
space is, essentially, a lattice, and you can have a discrete gauge group.

Ilja

[Ilja Schmelzer]

"LuRan" <hephooey@hotmail.com> schrieb
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?

If the underlying space is continuous, it usually makes not much sense to
consider discontinous gauge fields on it. But you have some internal
boundary things may be different.

Another interesting domain is lattice gauge theory. Here the underlying
space is, essentially, a lattice, and you can have a discrete gauge group.

Ilja

[Ilja Schmelzer]

"LuRan" <hephooey@hotmail.com> schrieb
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?

If the underlying space is continuous, it usually makes not much sense to
consider discontinous gauge fields on it. But you have some internal
boundary things may be different.

Another interesting domain is lattice gauge theory. Here the underlying
space is, essentially, a lattice, and you can have a discrete gauge group.

Ilja

[Phil]

"LuRan" <hephooey@hotmail.com> wrote in message
news:1130562915.154815.161460@z14g2000cwz.googlegr oups.com...
> Hi all,
>
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?
>

In continuum gauge theory the gauge transformations are assumed to be
continuous and differentiable. With derivatives of the gauge field in
the action it is hard to make use of discontinuous transformations, but
there is nothing to stop you imagining them.

In Lattice gauge theory space-time is discrete so the gauge
transformations are too. The gauge transformation can be applied
independently at each site of the lattice just as you wanted.

If you have not seen how gauge groups work in Lattice gauge theory it is
worth learning. With discrete space-time events the gauge theory is
expressed directly in terms of the group rather than its Lie algebra.
This means that the gauge group can also be any finite group so it can
be discrete at that level too.

The diffeomorphism groups of general relativity are another form of
gauge group. Those too can be made discrete on a discrete space-time by
extending to event-symmetry where the gauge group becomes just the
permutation group permuting events. This kind of symmetry is a feature
of the famous matrix models of M-theory and string theory.

[Phil]

"LuRan" <hephooey@hotmail.com> wrote in message
news:1130562915.154815.161460@z14g2000cwz.googlegr oups.com...
> Hi all,
>
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?
>

In continuum gauge theory the gauge transformations are assumed to be
continuous and differentiable. With derivatives of the gauge field in
the action it is hard to make use of discontinuous transformations, but
there is nothing to stop you imagining them.

In Lattice gauge theory space-time is discrete so the gauge
transformations are too. The gauge transformation can be applied
independently at each site of the lattice just as you wanted.

If you have not seen how gauge groups work in Lattice gauge theory it is
worth learning. With discrete space-time events the gauge theory is
expressed directly in terms of the group rather than its Lie algebra.
This means that the gauge group can also be any finite group so it can
be discrete at that level too.

The diffeomorphism groups of general relativity are another form of
gauge group. Those too can be made discrete on a discrete space-time by
extending to event-symmetry where the gauge group becomes just the
permutation group permuting events. This kind of symmetry is a feature
of the famous matrix models of M-theory and string theory.

[Phil]

"LuRan" <hephooey@hotmail.com> wrote in message
news:1130562915.154815.161460@z14g2000cwz.googlegr oups.com...
> Hi all,
>
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?
>

In continuum gauge theory the gauge transformations are assumed to be
continuous and differentiable. With derivatives of the gauge field in
the action it is hard to make use of discontinuous transformations, but
there is nothing to stop you imagining them.

In Lattice gauge theory space-time is discrete so the gauge
transformations are too. The gauge transformation can be applied
independently at each site of the lattice just as you wanted.

If you have not seen how gauge groups work in Lattice gauge theory it is
worth learning. With discrete space-time events the gauge theory is
expressed directly in terms of the group rather than its Lie algebra.
This means that the gauge group can also be any finite group so it can
be discrete at that level too.

The diffeomorphism groups of general relativity are another form of
gauge group. Those too can be made discrete on a discrete space-time by
extending to event-symmetry where the gauge group becomes just the
permutation group permuting events. This kind of symmetry is a feature
of the famous matrix models of M-theory and string theory.

[Phil]

"LuRan" <hephooey@hotmail.com> wrote in message
news:1130562915.154815.161460@z14g2000cwz.googlegr oups.com...
> Hi all,
>
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?
>

In continuum gauge theory the gauge transformations are assumed to be
continuous and differentiable. With derivatives of the gauge field in
the action it is hard to make use of discontinuous transformations, but
there is nothing to stop you imagining them.

In Lattice gauge theory space-time is discrete so the gauge
transformations are too. The gauge transformation can be applied
independently at each site of the lattice just as you wanted.

If you have not seen how gauge groups work in Lattice gauge theory it is
worth learning. With discrete space-time events the gauge theory is
expressed directly in terms of the group rather than its Lie algebra.
This means that the gauge group can also be any finite group so it can
be discrete at that level too.

The diffeomorphism groups of general relativity are another form of
gauge group. Those too can be made discrete on a discrete space-time by
extending to event-symmetry where the gauge group becomes just the
permutation group permuting events. This kind of symmetry is a feature
of the famous matrix models of M-theory and string theory.

[Phil]

"LuRan" <hephooey@hotmail.com> wrote in message
news:1130562915.154815.161460@z14g2000cwz.googlegr oups.com...
> Hi all,
>
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?
>

In continuum gauge theory the gauge transformations are assumed to be
continuous and differentiable. With derivatives of the gauge field in
the action it is hard to make use of discontinuous transformations, but
there is nothing to stop you imagining them.

In Lattice gauge theory space-time is discrete so the gauge
transformations are too. The gauge transformation can be applied
independently at each site of the lattice just as you wanted.

If you have not seen how gauge groups work in Lattice gauge theory it is
worth learning. With discrete space-time events the gauge theory is
expressed directly in terms of the group rather than its Lie algebra.
This means that the gauge group can also be any finite group so it can
be discrete at that level too.

The diffeomorphism groups of general relativity are another form of
gauge group. Those too can be made discrete on a discrete space-time by
extending to event-symmetry where the gauge group becomes just the
permutation group permuting events. This kind of symmetry is a feature
of the famous matrix models of M-theory and string theory.

[Phil]

"LuRan" <hephooey@hotmail.com> wrote in message
news:1130562915.154815.161460@z14g2000cwz.googlegr oups.com...
> Hi all,
>
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?
>

In continuum gauge theory the gauge transformations are assumed to be
continuous and differentiable. With derivatives of the gauge field in
the action it is hard to make use of discontinuous transformations, but
there is nothing to stop you imagining them.

In Lattice gauge theory space-time is discrete so the gauge
transformations are too. The gauge transformation can be applied
independently at each site of the lattice just as you wanted.

If you have not seen how gauge groups work in Lattice gauge theory it is
worth learning. With discrete space-time events the gauge theory is
expressed directly in terms of the group rather than its Lie algebra.
This means that the gauge group can also be any finite group so it can
be discrete at that level too.

The diffeomorphism groups of general relativity are another form of
gauge group. Those too can be made discrete on a discrete space-time by
extending to event-symmetry where the gauge group becomes just the
permutation group permuting events. This kind of symmetry is a feature
of the famous matrix models of M-theory and string theory.

[Phil]

"LuRan" <hephooey@hotmail.com> wrote in message
news:1130562915.154815.161460@z14g2000cwz.googlegr oups.com...
> Hi all,
>
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?
>

In continuum gauge theory the gauge transformations are assumed to be
continuous and differentiable. With derivatives of the gauge field in
the action it is hard to make use of discontinuous transformations, but
there is nothing to stop you imagining them.

In Lattice gauge theory space-time is discrete so the gauge
transformations are too. The gauge transformation can be applied
independently at each site of the lattice just as you wanted.

If you have not seen how gauge groups work in Lattice gauge theory it is
worth learning. With discrete space-time events the gauge theory is
expressed directly in terms of the group rather than its Lie algebra.
This means that the gauge group can also be any finite group so it can
be discrete at that level too.

The diffeomorphism groups of general relativity are another form of
gauge group. Those too can be made discrete on a discrete space-time by
extending to event-symmetry where the gauge group becomes just the
permutation group permuting events. This kind of symmetry is a feature
of the famous matrix models of M-theory and string theory.

[Phil]

"LuRan" <hephooey@hotmail.com> wrote in message
news:1130562915.154815.161460@z14g2000cwz.googlegr oups.com...
> Hi all,
>
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?
>

In continuum gauge theory the gauge transformations are assumed to be
continuous and differentiable. With derivatives of the gauge field in
the action it is hard to make use of discontinuous transformations, but
there is nothing to stop you imagining them.

In Lattice gauge theory space-time is discrete so the gauge
transformations are too. The gauge transformation can be applied
independently at each site of the lattice just as you wanted.

If you have not seen how gauge groups work in Lattice gauge theory it is
worth learning. With discrete space-time events the gauge theory is
expressed directly in terms of the group rather than its Lie algebra.
This means that the gauge group can also be any finite group so it can
be discrete at that level too.

The diffeomorphism groups of general relativity are another form of
gauge group. Those too can be made discrete on a discrete space-time by
extending to event-symmetry where the gauge group becomes just the
permutation group permuting events. This kind of symmetry is a feature
of the famous matrix models of M-theory and string theory.

[Phil]

"LuRan" <hephooey@hotmail.com> wrote in message
news:1130562915.154815.161460@z14g2000cwz.googlegr oups.com...
> Hi all,
>
> I know it sounds a little bit stupid, but this problem keeps bothering
> me. Are there any discrete gauge transformations? I mean, can I just
> transform the phase of some discrete points in the spacetime and keep
> the phase of other points fixed. This may be difficult to express in a
> mathematical form, but I see no reason from the gauge principle that
> these kind of transform should not exist. But all the textbooks and
> papers seem assume the gauge transformation should be continue from the
> beginning, Any ideas?
>

In continuum gauge theory the gauge transformations are assumed to be
continuous and differentiable. With derivatives of the gauge field in
the action it is hard to make use of discontinuous transformations, but
there is nothing to stop you imagining them.

In Lattice gauge theory space-time is discrete so the gauge
transformations are too. The gauge transformation can be applied
independently at each site of the lattice just as you wanted.

If you have not seen how gauge groups work in Lattice gauge theory it is
worth learning. With discrete space-time events the gauge theory is
expressed directly in terms of the group rather than its Lie algebra.
This means that the gauge group can also be any finite group so it can
be discrete at that level too.

The diffeomorphism groups of general relativity are another form of
gauge group. Those too can be made discrete on a discrete space-time by
extending to event-symmetry where the gauge group becomes just the
permutation group permuting events. This kind of symmetry is a feature
of the famous matrix models of M-theory and string theory.