What is Invariant: Definition and 405 Discussions

Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions. Classically, the theory dealt with the question of explicit description of polynomial functions that do not change, or are invariant, under the transformations from a given linear group. For example, if we consider the action of the special linear group SLn on the space of n by n matrices by left multiplication, then the determinant is an invariant of this action because the determinant of A X equals the determinant of X, when A is in SLn.

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  1. D

    Why does the Earth move around the sun?

    I say the only viewpoint available that provides us with the truth is the center of mass. You go ahead be my guest and choose another but be ware: Your physics will not remain the same. Let's fix the coordinate system on the sun and watch the Earth moving. The sun is truly immovable thus has no...
  2. wolram

    Is Fine Structure Invariant Over Cosmological Time Scales?

    http://arxiv.org/PS_cache/astro-ph/pdf/0401/0401094.pdf a 24 page paper on the "FINE STRUCTURE", concludes that it is invariant over cosmological time scales.
  3. M

    Maxwell's eqn in invariant form

    Maxwell's eqn, in invariant form reads: F^{\mu \nu}{}_{;\nu} = J^{\mu} and F_{\alpha \beta ;\gamma} + F_{\beta \gamma ;\alpha}+F_{\gamma \alpha; \beta} = 0 Can someone give Maxwell's eqn if there is magnetic charge and current? I do not believe the form (matrix element) of F change...
  4. P

    Observer Dependant vs Invariant

    "Observer Dependant" vs "Invariant" The point I want to make in this thread is on something with is rather subtle. Define the quantity, m, as the quantity such that, in an inertial frame, mv is conserved. Call this quantity "mass" (some call this "relativistic mass") For tardyon's...
  5. P

    Invariant Mass vs Proper Mass

    "Invariant Mass" vs "Proper Mass" I see that there are many people here who prefer the idea that the mass of a particle is the magnitude of the the particle's 4-momentum. However that is known as "Proper Mass" and some simply say "mass." However that idea is limited in use. It can't be...
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