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This paper presents some methods of representing canonical commutation relations in terms of hyperfinite-dimensional matrices, which are constructed by nonstandard analysis. The first method uses representations of a nonstandard extension…
We describe a general conjecture on how one may derive from the generic bosonic case all structural properties of multivariate diagonal coinvariant modules in $k$ sets of $n$ commuting variables (bosons), and $j$ sets of $n$ anticommuting…
We analyze some features of alternative Hermitian and quasi-Hermitian quantum descriptions of simple and bipartite compound systems. We show that alternative descriptions of two interacting subsystems are possible if and only if the metric…
It is shown that any two Hamiltonians H(t) and H'(t) of N dimensional quantum systems can be related by means of time-dependent canonical transformations (CT). The dynamical symmetry group of system with Hamiltonian H(t) coincides with the…
In this paper we study families of complex Hermite polynomials and construct deformed versions of them, using a $GL(2,\mathbb{C})$ transformation. This construction leads to the emergence of biorthogonal families of deformed complex Hermite…
We extend the recently developed kinematical framework for diffeomorphism invariant theories of connections for compact gauge groups to the case of a diffeomorphism invariant quantum field theory which includes besides connections also…
We exploit the standard tools and techniques of the augmented version of Bonora-Tonin (BT) superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST and (anti-)co-BRST symmetry transformations for the…
The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a…
In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries and conserved quantities in the language of commutant algebras. In particular, we start with families of…
We introduce both an exactly solvable model and a coupled-layer construction for an exotic, three-dimensional phase of matter with immobile topological excitations that carry a protected internal degeneracy. Unitary transformations on this…
We introduce a class of pseudo-bosonic Klein-Gordon fields in 1+1 dimensions and we discuss some of their properties. This work originates from non Hermitian quantum mechanics and deformed canonical commutation relations. We show that,…
The relevance in Physics of non-Hermitian operators with real eigenvalues is being widely recognized not only in quantum mechanics but also in other areas, such as quantum optics, quantum fluid dynamics and quantum field theory. %stochastic…
We propose two alternative formulations for a three-dimensional non-anticommutative superspace in which some of the fermionic coordinates obey Clifford anticommutation relations. For this superspace, we construct the supersymmetry…
Superstrings have been postulated based on parafermionic partition functions which permit spacetime supersymmetry by generalized Jacobi identities. A comprehensive search finds new such identities. Quadrilateral anomaly cancellation gives…
The article studies the extension of the internal spaces of fermion and boson second quantized fields, described by the superposition of odd (for fermions) and even (for bosons) products of the operators $\gamma^ {a}$, to strings and odd…
A new model of supersymmetry between bosons and fermions is proposed. Its representation space is spanned by states with PT symmetry and real energies but the inter-related partner Hamiltonians themselves remain complex and non-Hermitian.…
We show how an induced invariance of the massless particle action can be used to construct an extension of the Heisenberg canonical commutation relations in a non-commutative space-time.
In the Light-Front Dynamics, the wave function equations and their numerical solutions, for two fermion bound systems, are presented. Analytical expressions for the ladder one-boson exchange interaction kernels corresponding to scalar,…
We consider the noncommutative extension of the BF theory in two spacetime dimensions. We show that the introduction of the noncommutative parameter \theta_{\mu\nu}, already at first order in the analytical sector, induces infinitely many…
We study quantum many-body states of immanons, hypothetical particles that obey an exchange symmetry defined for more than two participating particles. Immanons thereby generalize bosons and fermions, which are defined by their behavior…