Questions tagged [group-theory]

Group theory is a branch of abstract algebra. A group is a set of objects, together with a binary operation, that satisfies four axioms. The set must be closed under the operation and contain an identity object. Every object in the set must have an inverse, and the operation must be associative. Groups are used in physics to describe symmetry operations of physical systems.

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Does the set of evolution operators in QM form any known algebraic structure (e.g., a monoid)?

The evolution operator, $U(t,t_0)$, in quantum mechanics is defined by $$|\Psi(t)\rangle = U(t,t_0)|\Psi(t_0)\rangle.$$ with $t\geq t_0$. Is the set of such evolution operators, specified by two ...
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How to find Casimir operator eigenvalues of $SU(N)$? [closed]

The $[f1, f2, f3…fn]$ in the image represent the irreducible representations of $SU[n]$. How to find the irreducible representations of $SU[n]$ that conform to the form $[f1, f2...fn]$. Can you give ...
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Does all symmetry breaking have corresponding unitary group?

In high energy physics. Symmetry breaking like electroweak's has corresponding $SU(2)\times U(1)$ unitary gauge group broken down to $U(1)$. Does it mean all kinds of symmetry breaking (even low ...
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Is the factorization method of Hamiltonian related to the theory of Lie groups?

I was learning about algebraic methods to solve the H atom, when I came across the factorization method. It is mentioned in various textbooks, notes and papers, like the one from Infeld and Hull. I am ...
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One-Loop beta function for gauge couplings

I am currently doing my homework on Standard Model one-loop correction. When I am reading Quantum Field Theory by Mark Srednicki and Journeys Beyond the Standard Model by Pierre Ramond, I notice some ...