Related papers: Multi-particle Representations of the Poincar\'e G…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
This paper introduces a Heisenberg picture approach to Matrix Product States (MPS), offering a rigorous yet intuitive framework to explore their structure and classification. MPS efficiently represent ground states of quantum many-body…
The use of the hyperspherical harmonic (HH) basis in the description of bound states in an $A$-body system composed by identical particles is normally preceded by a symmetrization procedure in which the statistic of the system is taken into…
We investigate the conditions under which particle multiplicities in high energy collisions are Boltzmann distributed, as is the case for hadron production in e^+e^-, pp, p-pbar and heavy ion collisions. We show that the apparent…
The relativistic quantum field theory is the unique theory that combines the relativity and quantum theory and is invariant under the Poincar\'e transformation. The ground state, vacuum, is singlet and one particle states are transformed as…
The Hilbert space H^3q of the three quarks with one excited quark is decomposed into Lorentz group representations. It is shown that the quantum numbers of the reported and ``missing'' resonances fall apart and populate distinct…
Why massless particles, for example photons, can only have two helicity one-particle states is the main subject of this work. As we know, the little group which describes massive particle one-particle states' transformations under the…
Even simplified models of quantum many-body systems can be difficult to analyse. However, taking inspiration from the foundations of physics, one may wonder whether there are practical advantages to constructing alternative beyond-quantum…
We present a novel, non-parametric form for compactly representing entangled many-body quantum states, which we call a `Gaussian Process State'. In contrast to other approaches, we define this state explicitly in terms of a configurational…
We investigate the many-body states of exciton-polaritons that can be observed by pump-probe spectroscopy. Here, a weak-probe `spin-down' polariton is introduced into a coherent state of `spin-up' polaritons created by a strong pump. We…
We prove the Bisognano-Wichmann property for asymptotically complete Haag-Kastler theories of massless particles. These particles should either be scalar or appear as a direct sum of two opposite integer helicities, thus, e.g., photons are…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
One of pressing problems in mathematical physics is to find a generalized Poincar\'e symmetry that could be applied to nonflat space-times. As a step in this direction we define the semidirect product of groupoids $\Gamma_0 \rtimes…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
In relativistic quantum mechanics, elementary particles are described by irreducible unitary representations of the Poincare group. The same applies to the center-of-mass kinematics of a multi-particle system that is not subject to external…
A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be…
Development of quantum engineering put forward new theoretical problems. Behavior of a single mesoscopic cell (device) we may usually describe by equations of quantum mechanics. However if experimentators gather hundreds of thousands of…
A new model of relativistic massive particle with arbitrary spin (($m,s$)-particle) is suggested. Configuration space of the model is a product of Minkowski space and two-dimensional sphere, ${\cal M}^6 = {\Bbb R}^{3,1} \times S^2$. The…
We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem,…
Scattering processes in high-energy physics are inherently quantum mechanical, yet are typically analyzed at the level of final states, where entanglement appears as a property of the outcome rather than a consequence of the underlying…