Related papers: Lorentz and permutation invariants of particles I
We present an in-depth investigation of the ${\rm SL}(2,\mathbb{R})$ momentum space describing point particles coupled to Einstein gravity in three space-time dimensions. We introduce different sets of coordinates on the group manifold and…
In this paper, we are interested in the moments of the characteristic polynomial $Z_n(x)$ of the $n\times n$ permutation matrices with respect to the uniform measure. We use a combinatorial argument to write down the generating function of…
The equations of motion of massive particles in GR are completely determined by the field equation. We utilize the particular form of Einstein's field equation and propose for the $N$-body problem of the equations that are Lorentz invariant…
The mathematical rules used to handle systems of identical quantum particles bring into question whether the elementary constituents of matter, such as electrons, have the fundamental characteristics of persistence and reidentifiability…
The one-particle distribution function is of importance both in non-relativistic and relativistic statistical physics. In the relativistic framework, Lorentz invariance is possibly its most fundamental property. The present article on the…
We describe how a stable effective theory in which particles of the same fermion number attract may spontaneously break Lorentz invariance by giving non-zero fermion number density to the vacuum (and therefore dynamically generating a…
The claim that a particle is an irreducible representation of the Poincar\'e group -- what I call \emph{Wigner's identification} -- is now, decades on from Wigner's (1939) original paper, so much a part of particle physics folklore that it…
This paper describes a particularly didactic and transparent derivation of basic properties of the Lorentz group. The generators for rotations and boosts along an arbitrary direction, as well as their commutation relations, are written as…
Noncommutative invariant theory is a generalization of the classical invariant theory of the action of $SL(2,\IC)$ on binary forms. The dimensions of the spaces of invariant noncommutative polynomials coincide with the numbers of certain…
Motivated by generalized uncertainty principle, we derive a discrete picture of the space that respects Lorentz symmetry as well as gauge symmetry through setting an equivalency between linear GUP correction term and electromagnetic…
Recent tentative experimental indications, and the subsequent theoretical speculations, regarding possible violations of Lorentz invariance have attracted a vast amount of attention. An important technical issue that considerably…
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
We say that permutations $\pi_1,\dots, \pi_r \in \mathcal{S}_n$ invariably generate $\mathcal{S}_n$ if, no matter how one chooses conjugates $\pi'_1,\dots,\pi'_r$ of these permutations, $\pi'_1,\dots,\pi'_r$ generate $\mathcal{S}_n$. We…
We study remaining Lorentz symmetry, i.e. Lorentz transformations which leave the noncommutativity parameter $\theta^{\mu\nu}$ invariant, within the approach of time-ordered perturbation theory (TOPT) to space-time noncommutative theories.…
Unlike in the case of distinguishable particles, the concept of entanglement-- not to mention, nonlocality-- remains debated in case of indistinguishable particles. Here, we show that certain existing all-versus-nothing type of proofs of…
Quantum mechanics ordinarily describes particles as being pointlike, in the sense that the uncertainty $\Delta x$ can, in principle, be made arbitrarily small. It has been shown that suitable correction terms to the canonical commutation…
A method is presented to obtain local unitary invariants for multipartite quantum systems consisting of fermions or distinguishable particles. The invariants are organized into infinite families, in particular, the generalization to higher…
We present an efficient algorithm for constructing all the matrix elements of covariant tensor currents of massless particles of arbitrary spins in the covariant formulation. The construction of matrix elements can be taken simply by…
Bernoulli-$p$ thinning has been well-studied for point processes. Here we consider three other cases: (1) sequences $(X_1,X_2,...)$; (2) gaps of such sequences $(X_{n+1}-X_1)_{n\in\mathbb{N}}$; (3) partition structures. For the first case…
It is shown how bosonic material particles can emerge from a covariant formulation of de Broglie-Bohm theory. The formulation is based on the work of Nikolic. Material particles are continuous fields, formed as the eigenvalue of the…