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2. Non-Hermitian quantum mechanics - Wikipedia

   en.wikipedia.org/wiki/Non-Hermitian_quantum...

   The first paper that has "non-Hermitian quantum mechanics" in the title was published in 1996 [1] by Naomichi Hatano and David R. Nelson. The authors mapped a classical statistical model of flux-line pinning by columnar defects in high-T c superconductors to a quantum model by means of an inverse path-integral mapping and ended up with a non-Hermitian Hamiltonian with an imaginary vector ...

3. Exceptional point - Wikipedia

   en.wikipedia.org/wiki/Exceptional_point

   For non-Hermitian quantum systems with PT symmetry, fidelity can be used to analyze whether exceptional points are of higher-order. Many numerical methods such as the Lanczos algorithm , Density Matrix Renormalization Group (DMRG), and other tensor network algorithms are relatively easy to calculate only for the ground state, but have many ...

4. Symmetry in quantum mechanics - Wikipedia

   en.wikipedia.org/wiki/Symmetry_in_quantum_mechanics

   In quantum electrodynamics, the local symmetry group is U(1) and is abelian. In quantum chromodynamics, the local symmetry group is SU(3) and is non-abelian. The electromagnetic interaction is mediated by photons, which have no electric charge. The electromagnetic tensor has an electromagnetic four-potential field possessing gauge symmetry.

5. Lorentz group - Wikipedia

   en.wikipedia.org/wiki/Lorentz_group

   The Lorentz group is a six-dimensional noncompact non-abelian real Lie group that is not connected. The four connected components are not simply connected. [1] The identity component (i.e., the component containing the identity element) of the Lorentz group is itself a group, and is often called the restricted Lorentz group, and is denoted SO ...

6. CPT symmetry - Wikipedia

   en.wikipedia.org/wiki/CPT_symmetry

   CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level. [1] [2] The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.

7. Mathematical formulation of the Standard Model - Wikipedia

   en.wikipedia.org/wiki/Mathematical_formulation...

   The free field model can be solved exactly, and then the solutions to the full model can be expressed as perturbations of the free field solutions, for example using the Dyson series. It should be observed that the decomposition into free fields and interactions is in principle arbitrary.

8. Hermitian symmetric space - Wikipedia

   en.wikipedia.org/wiki/Hermitian_symmetric_space

   In general a Hermitian symmetric space gives rise to a 3-graded Lie algebra with a period 2 conjugate linear automorphism switching the parts of degree ±1 and preserving the degree 0 part. This gives rise to the structure of a Jordan pair or hermitian Jordan triple system, to which Loos (1977) extended the theory of Jordan algebras. All ...

9. Classical group - Wikipedia

   en.wikipedia.org/wiki/Classical_group

   The term "classical group" was coined by Hermann Weyl, it being the title of his 1939 monograph The Classical Groups. [3] The classical groups form the deepest and most useful part of the subject of linear Lie groups. [4] Most types of classical groups find application in classical and modern physics. A few examples are the following.