Any EM-field in terms of photon

[olgerm]

I think I just understood something, that I wanted to have explained to me 3 years ago: bra and kets include numbers that describe the states that system can be in. What every number means is not specified, but can vary in every model(must be same everywhere in same model). Is it correct?

Maybe it is misconseption, but I have always thought, that QFT describes particles as fields so that probability of particle being a position is determined by the field value in that point. What ever are relations between these fields are should be describeable by equation between those fields. I can't think of any realtion between fields that can be described by hamilonian, but can not be described by (differencial) equations between the fields. Maybe brackets are more useful in systems that have constraint "forces", but for fields only it should be possible to write it without using hamiltonian.

 

[HomogenousCow]

Quantum mechanics isn’t a change of notation, it’s a fundamentally different physical framework from classical mechanics. You don’t have to use the bra-ket notation but you must learn quantum mechanics to gleam any understanding on the subject.

The Hamiltonian is simply the generator of time-translation (evolving systems forwards/backwards in time) and appears in all frameworks of physics whether directly or indirectly. The classical theory of fields that you seem to be talking about can also be formulated in terms of Hamiltonians but this is not done because it is not as elegant or simple as the Lagrangian approach.

 

[olgerm]

Quantum mechanics isn’t a change of notation, it’s a fundamentally different physical framework from classical mechanics. You don’t have to use the bra-ket notation but you must learn quantum mechanics to gleam any understanding on the subject.

I know. I have been looking for sources that do not use bra-ket notation. Even better if it did not use hamiltonian ether.

 

[HomogenousCow]

While I question this approach, I guess you could learn QM from the path integral approach first. However it doesn’t seem apparent to me why you shouldn’t learn QM the way everyone else does, since it’s that way for good reason.

 

[olgerm]

why you shouldn’t learn QM the way everyone else does, since it’s that way for good reason.

It is not that I do want to learn it in specific way, but that I can't understand the sources that use brakets, operators, and commutivity. I have wanted someone to explain me what these mean or give me clear refence to look it up. I now finally understood something(post 31), but still not enougth.
I don't think any of my learning has been hinder by insufficient knowledge in QM, but by not understanding meaning of brakets, operators, and commutivity.

Is there really something about quantum field that can not be expressed without hamiltonian and brakets, but only by fields and differencial equations?

 

[PeterDonis]

I don't think any of my learning has been hinder by insufficient knowledge in QM, but by not understanding meaning of brakets, operators, and commutivity.

I don't understand how you can have sufficient knowledge of QM if you don't understand bras and kets, operators, and commutativity, since all of those are basic concepts that are used to describe QM. And, as has already been noted, QM textbooks all go into these subjects. If you work through a QM textbook and find difficulty in understanding something specific it says about bras and kets, operators, or commutativity, you can start a new thread asking about that specific thing. Asking for someone to explain, in general, bras and kets, operators, and commutativity is asking for someone to give you a course in QM, which is way beyond the scope of a PF discussion. If you want such a course, you need to go take one, or find course materials online (for example, MIT's Open Courseware) and work through them.

Thread closed.