Related papers: Spin, Statistics, and Reflections, II. Lorentz Inv…
The universal covering of SO(3) is modelled as a reflection group G_R in a representation independent fashion. For relativistic quantum fields, the Unruh effect of vacuum states is known to imply an intrinsic form of reflection symmetry,…
We derive the spin-statistics theorem in both relativistic and non-relativistic first-quantized form, extending considerably the earlier proofs. Our derivation is based on the representation theories of the groups SU (2) and SL(2,C), latter…
The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.
The spin-statistics conection is obtained for classical point particles. The connection holds within pseudomechanics, a theory of particle motion that extends classical physics to include anticommuting Grassmann variables, and which…
We have shown that Reflection Symmetric transformation is Lorentz invariant. It ia also associative. We have also shown that Reflection Symmetric sum of vectors has a spin-like term comparable to the spin of Dirac eletron. We have found…
A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is…
In this paper we postulate an algebraic model to explain how the symmetry of three lepton species plays its role in the Lorentz extension. Inspired by the two-to-one mapping between the group SL (2, C) and the Lorentz group, we design a…
The connection between spin and statistics implied by the continuous Lorentz group together with strong reflection (TCP) is shown to hold also for the q-Lorentz group.
Lorentz's group represented by the hypercomplex system of numbers, which is based on dirac matrices, is investigated. This representation is similar to the space rotation representation by quaternions. This representation has several…
We consider the quantum spin ice models in the planar pyrochlore lattice. The models are obtained by perturbing the Ising model with different lattice symmetry preserving quantum fluctuations. We map these models to a compact U(1) lattice…
The CPT theorem states that a unitary and Lorentz-invariant theory must also be invariant under a discrete symmetry $\mathbf{CRT}$ which reverses charge, time, and one spatial direction. In this article, we study a $\mathbb{Z}_2 \times…
It is shown that a subgroup of $SL(2,{\mathbb H})$, denoted $Spin(2,{\mathbb H})$ in this paper, which is defined by two conditions in addition to unit quaternionic determinant, is locally isomorphic to the restricted Lorentz group,…
We construct the double copy of the chiral higher-spin theory. It is a Lorentz invariant theory with the little group spectrum given by the tensor square of the chiral higher-spin theory spectrum. Moreover, its interactions factorise in…
The statistics of soliton sectors of massive 2D field theories is analysed. In the soliton field algebra, the non-local commutation relations are determined and Weak Locality, Spin-Statistics and CPT theorems are proven. These theorems…
Recently, Cohen and Glashow pointed out that all known experimental tests of relativistic kinematics are consistent with invariance of physics under the four-parameter subgroup Sim(2) of the Lorentz group. The massive one-particle…
It is shown that a unitary translationally invariant field theory in (1+1) dimensions satisfying isotropic scale invariance, standard assumptions about the spectrum of states and operators and the requirement that signals propagate with…
A spin-statistics theorem and a PCT theorem are obtained in the context of the superselection sectors in Quantum Field Theory on a 4-dimensional space-time. Our main assumption is the requirement that the modular groups of the von Neumann…
We continue the program, presented in previous Symposia, of discretizing physical models. In particular we calculate the integral Lorentz transformations with the help of discrete reflection groups, and use them for the covariance of…
The quantum concurrence of $SU(2) \otimes SU(2)$ spin-parity states is shown to be invariant under $SO(1,3)$ Lorentz boosts and $O(3)$ rotations when the density matrices are constructed in consonance with the covariant probabilistic…
A gauge theory of the Lorentz group with a mass-dimension one gauge field coupling to matter of any spin is developed. As a completely new feature the "Vierbein" assuring local gauge invariance enters not as an independent dynamical field,…