Related papers: Duality Induced Reflections and CPT
The motivations for the construction of an 8-component representation of fermion fields based on a two dimensional representation of time reversal transformation and CPT invariance are discussed. Some of the elementary properties of the…
We describe the representation theory of C*-crossed-products of a unital C*-algebra A by the cyclic group of order 2. We prove that there are two main types of irreducible representations for the crossed-product: those whose restriction to…
We discuss an interesting duality known to occur for certain complex reflection groups, namely the duality groups. Our main construction yields a concrete, representation theoretic realisation of this duality. This allows us to naturally…
The variational calculation of the two-electron reduced density matrix (2-RDM) is extended to periodic molecular systems. If the 2-RDM theory is extended to the periodic case without consideration of time-reversal symmetry, however, it can…
In the present paper, we derive formulas of complex and $\ell$-adic multiple polylogarithms, which have two aspects: a duality in terms of indexes and a reflection in terms of variables. We provide an algebraic proof of these formulas by…
This article shows that for unitary dual reductive pairs the first occurrence of theta lift of an irreducible cuspidal automorphic representation is irreducible. It also proves a refined tower property for theta lifts and the involutive…
We consider the $O(3)$ nonlinear sigma model with the $\theta$-term and its linear counterpart in 1+1D. The model has discrete time-reflection and space-reflection symmetries at any $\theta$, and enjoys the periodicity in $\theta\rightarrow…
For a large class of Abelian lattice models with sign problems, including the case of non-zero chemical potential, duality maps models with complex actions into dual models with real actions. For extended regions of parameter space,…
We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized…
We study irreducible spherical unitary representations of the Drinfeld double of a $q$-deformation of a connected simply connected compact Lie group, which can be considered as a quantum analogue of the complexification of the Lie group. In…
After analyzing the implication of investigations on the C, P and T transformations since 1956, we propose that there is a basic symmetry in particle physics. The combined space-time inversion is equivalent to particle-antiparticle…
We develop a common semantic framework for the interpretation both of $\mathbf{IPC}$, the intuitionistic propositional calculus, and of logics weaker than $\mathbf{IPC}$ (substructural and subintuitionistic logics). This is done by proving…
We show that the CPT group of the Dirac field emerges naturally from the PT and P (or T) subgroups of the Lorentz group.
Let $G$ be a classical group $\GL(n)$, $\oU(n)$, $\oO(n)$ or $\Sp(2n)$, over a non-archimedean local field of characteristic zero. Let $\pi$ be an irreducible admissible smooth representation of $G$. It is well known that the contragredient…
We derive the implications of particle-vortex duality for the electromagnetic response of Quantum Hall systems beyond the linear-response regime. This provides a first theoretical explanation of the remarkable duality which has been…
We consider the phase-space of Yang-Mills on a cylindrical space-time ($S^1 \times {\bf R}$) and the associated algebra of gauge-invariant functions, the $T$-variables. We solve the Mandelstam identities both classically and…
Loop-Tree Duality (LTD) is a framework in which the energy components of all loop momenta of a Feynman integral are integrated out using residue theorem, resulting in a sum over tree-like structures. Originally, the LTD expression exhibits…
The action for a massless particle in 4D Minkowski space has a worldline time-reversing symmetry corresponding to CPT invariance of the quantum theory. The analogous symmetry of the N-extended superparticle is shown to be anomalous when N…
Selfdual representations of any group fall into two classes when they are irreducible: those which carry a symmetric bilinear form, and the others which carry an alternating bilinear form. The Langlands correspondence, which matches the…
Previously, we demonstrated that the dynamics of kicked spin chains possess a remarkable duality property. The trace of the unitary evolution operator for $N$ spins at time $T$ is related to one of a non-unitary evolution operator for $T$…