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Free quantum field theories on curved backgrounds are discussed via three explicit examples: the real scalar field, the Dirac field and the Proca field. The first step consists of outlining the main properties of globally hyperbolic…
A generalized Schwinger boson representation is proposed to describe the two-dimensional SU(4) symmetric spin-orbital quantum antiferromagnet. A uniform mean field solution gives rise to an antiferromagnetic long range ordered state with a…
The (in)finite dimensional symplectic group of homogeneous canonical transformations is represented on the bosonic Fock space by the action of the group on the ultracoherent vectors, which are generalizations of the coherent states.
The canonical quantization of the tachyon field is suggested. Quantization is based on the conception of stable and unstable components of the tachyon degrees of freedom.
The quantization rules recently proposed by M. Navarro (and independently I.V. Kanatchikov) for a finite-dimensional formulation of quantum field theory are applied to the Klein-Gordon and the Dirac fields to obtain the quantum equations of…
Analog quantum simulation has the potential to be an indispensable technique in the investigation of complex quantum systems. In this work, we numerically investigate a one-dimensional, faithful, analog, quantum electronic circuit simulator…
The canonical quantum theory of a free field using arbitrary foliations of a flat two-dimensional spacetime is investigated. It is shown that dynamical evolution along arbitrary spacelike foliations is unitarily implemented on the same Fock…
Bosons and fermions are described by using canonical generators of Cuntz algebras on any permutative representation. We show a fermionization of bosons which universally holds on any permutative representation of the Cuntz algebra ${\cal…
Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold'' . Such discretization by…
The Jordan-Wigner transformation is traditionally applied to one dimensional systems, but recent works have generalized the transformation to fermionic lattice systems in higher dimensions while keeping locality manifest. These developments…
Canonical transformations (Bogoliubov transformations) for fermions with an infinite number of degrees of freedom are studied within a calculus of superanalysis. A continuous representation of the orthogonal group is constructed on a…
We review a recently proposed SuperGeometric (SG) approach to Quantum Field Theories (QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. By adopting natural choices for the…
We show that a canonical tranformation converts, up to a boundary term, a generic 2d dilaton gravity model into a bosonic string theory with a Minkowskian target space.
We establish that the recently discovered fermionic T-duality can be viewed as a canonical transformation in phase space. This requires a careful treatment of constrained Hamiltonian systems. Additionally, we show how the canonical…
Canonical quantization of quantum field theory models is inherently related to the Lorentz invariant partition of classical fields into the positive and the negative frequency parts $u(x) = u^+(x) + u^-(x),$ performed with the help of…
The non-relativistic Chern-Simons theory with the single-valued anyonic field is proposed as an example of q-deformed field theory. The corresponding q-deformed algebra interpolating between bosons and fermions,both in position and momentum…
We present a study on linear canonical transformation in the framework of a phase space representation of quantum mechanics that we have introduced in our previous work [1]. We begin with a brief recall about the so called phase space…
We consider the problem of bosonizing supersymmetric quantum mechanics (SSQM) and some of its variants, i.e., of realizing them in terms of only boson-like operators without fermion-like ones. In the SSQM case, this is realized in terms of…
Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive…
Motivated by the Goldbach conjecture in Number Theory and the abelian bosonization mechanism on a cylindrical two-dimensional spacetime we study the reconstruction of a real scalar field as a product of two real fermion (so-called…