Related papers: Spin, Statistics, and Reflections, I. Rotation Inv…
In the literature on quantum reference frames, the internal (relative) properties of a system are defined as those which are preserved under an arbitrary change of reference frame. For a system of quantum spins, these are all properties…
This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to…
The structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group is related to a notion of Hilbert modules endowed with inner products taking values in spaces of unbounded operators. A…
We survey theoretical and experimental/observational results on general-relativistic spin (rotation) effects in binary systems. A detailed discussion is given of the two-body Kepler problem and its first post-Newtonian generalization,…
We implement an extended version of reflection positivity (Wick-rotated unitarity) for invertible topological quantum field theories and compute the abelian group of deformation classes using stable homotopy theory. We apply these field…
Wigner's little groups are the subgroups of the Lorentz group whose transformations leave the momentum of a given particle invariant. They thus define the internal space-time symmetries of relativistic particles. These symmetries take…
This is mainly a lecture note taken by myself following Weinberg's book, but also contains some corrections to the abuse of mathematical treatment. This article discusses projective unitary representations of Poincare group on the single…
The article is a natural continuation of our paper {\em Quantum scalar field in FRW Universe with constant electromagnetic background}, Int. J. Mod. Phys. {\bf A12}, 4837 (1997). We generalize the latter consideration to the case of massive…
A Galilean Chern-Simons field theory is formulated for the case of two interacting spin-1/2 fields of distinct masses M and M'. A method for the construction of states containing N particles of mass M and N' particles of mass M' is given…
The standard quantum states of $n$ complex Grassmann variables with a free-particle Lagrangian transform as a spinor of SO(2n). However, the same `free-fermion' model has a non-linearly realized $SU(n|1)$ symmetry; it can be viewed as the…
A non-unitary version of quantum scattering is studied via an exactly solvable toy model. The model is merely asymptotically local since the smooth path of the coordinate is admitted complex in the non-asymptotic domain. At any real…
We consider models with a noncompact symmetry in the framework of $\mathcal{N}=1$ supersymmetry. Contrary to the conventional approach, the noncompact symmetry is realized linearly on all fields without constraints. The models are…
Having in mind the significance of parity (reflection) in various areas of physics, the single-mode and two-mode Wigner algebras are considered adding to them a reflection operator. The associated deformed $sl(2, R)$ algebra,…
It is common to use Galilean rotational transformation to investigate the Unruh effect for uniformly rotating observers. However, the rotating observer in this subject is an eccentric observer while Galilean rotational transformation is…
We analyze $SO(N)$ and $SU(N)$ gauge theories with scalars in adjoint and fundamental representations, coupled to renormalisable, classically scale invariant gravity. In the specific case of $SO(12),$ we show that the quantum field theory…
We develop the theory of Wigner representations for general probabilistic theories (GPTs), a large class of operational theories that include both classical and quantum theory. The Wigner representations that we introduce are a natural way…
For applications of group theory in quantum mechanics, one generally needs explicit matrix representations of the spectrum generating algebras that arise in bases that reduce the symmetry group of some Hamiltonian of interest. Here we use…
We construct a non-linear theory of interacting spin-2 fields that is invariant under the partially massless (PM) symmetry to all orders. This theory is based on the SO(1,5) group, in analogy with the SO(2,4) formulation of conformal…
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall…
We analyze some features of the entanglement entropy for an integer quantum Hall state ($\nu =1 $) in comparison with ideas from relativistic field theory and noncommutative geometry. The spectrum of the modular operator, for a restricted…