Related papers: Telling compositeness at a distance with outer aut…

Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer…

It is explained that the Standard Model combined charge conjugation and parity transformation (CP) is a simultaneous complex conjugation outer automorphism transformation of gauge and space-time symmetries. Simple examples are given for the…

We discuss anomalies associated with outer automorphisms in gauge theories based on classical groups, namely charge conjugations for $SU(N)$ and parities for $SO(2r)$. We emphasize the inequivalence (yet related by a flavor transformation)…

We give a concise presentation for the group of pure symmetric outer automorphisms of a given splitting of a free product $G_{1}\ast\dots\ast G_{n}$. These are the (outer) automorphisms which preserve the conjugacy classes of the free…

We give a consistent definition of generalised CP transformations in the context of discrete flavour symmetries. Non-trivial consistency conditions imply that every generalised CP transformation can be interpreted as a representation of an…

For a finite group G of Lie type and a prime p, we compare the automorphism groups of the fusion and linking systems of G at p with the automorphism group of G itself. When p is the defining characteristic of G, they are all isomorphic,…

The purpose of the present paper is twofold. In the first part, we provide an algebraic characterization of several families of $\nu= \frac{1}{2^n}$ $n\leq 5$ BPS states in M theory, at threshold and non-threshold, by an analysis of the BPS…

We discuss the origin of CP violation in settings with a discrete (flavor) symmetry $G$. We show that physical CP transformations always have to be class-inverting automorphisms of $G$. This allows us to categorize finite groups into three…

We study physical implications of general CP symmetry including CP-like symmetry. Various scattering amplitudes of CP asymmetry are calculated in CP-like symmetric models. We explicitly show that the CP-like transformation leads to a…

An automorphism of a group is called outer if it is not an inner automorphism. Let $G$ be a finite $p$-group. Then for every outer $p$-automorphism $\phi$ of $G$ the subgroup $C_G(\phi)=\{x\in G \;|\; x^\phi=x\}$ has order $p$ if and only…

Various approximate symmetries exist in nature. For example, the flavor $SU(4)$ symmetry involving the $up/down/strange/charm$ quarks is severely broken, the flavor $SU(3)$ symmetry involving the $up/down/strange$ quarks is moderately…

There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states $\mathbf{P}$ -- i.e., the set of one-dimensional projections on a complex Hilbert space $H$ -- and the…

Genuine tests of an asymmetry under T and/or CPT transformations imply the interchange between in-states and out-states. I explain a methodology to perform model-indepedent separate measurements of the three CP, T and CPT symmetry…

In this article, we further explore the nature of a connection between the groups of automorphisms of full shift spaces and the groups of outer automorphisms of the Higman--Thompson groups $\{G_{n,r}\}$. We show that the quotient of the…

It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…

An algebraic description of basic discrete symmetries (space inversion P, time reversal T, charge conjugation C and their combinations PT, CP, CT, CPT) is studied. Discrete subgroups {1,P,T,PT} of orthogonal groups of multidimensional…

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple…

Let R a be countable ergodic equivalence relation of type II_1 on a standard probability space (X,m). The group Out(R) of outer automorphisms of R consists of all invertible Borel measure preserving maps of the space which map R-classes to…

We study the existence of diagonal representatives in each equivalence class of representation matrices of boundary conditions in $SU(n)$ or $U(n)$ gauge theories compactified on the orbifolds $T^2/{\mathbb Z}_N$ ($N = 2, 3, 4, 6$). We…

This work is an enquiry into the circumstances under which entropy methods can give an answer to the questions of both quantum separability and classical correlations of a composite state. Several entropy functionals are employed to examine…