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A consistent local approach to the study of interacting relativistic fermion systems with a condensation of bare particles in its ground or vacuum state, which may has a finite matter density, is developed. The attention is payed to some of…
We study soliton solutions in supersymmetric scalar field theory with a class of potentials. We study both bosonic and fermionic zero-modes around the soliton solution. We study two possible couplings of gauge fields to these models. While…
Corresponding to a finite dimensional Hilbert space $H$ with $\dim H=n$, we define a geometric algebra $\gscript (H)$ with $\dim\sqbrac{\gscript (H)}=2^n$. The algebra $\gscript (H)$ is a Hilbert space that contains $H$ as a subspace. We…
Dualities provide deep insight into physics by relating two seemingly distinct theories. Here we propose and elaborate on a novel duality between bosonic and fermionic theories in four spacetime dimensions. Starting with a Euclidean lattice…
We formulate quantum field theories of massive fields of arbitrary spins. The presence of both physical and fake particles, organized into multiplets, makes it possible to fulfill the requirements of locality, unitarity and…
We study two-dimensional celestial conformal field theory describing four-dimensional ${\cal N}=1$ supergravity/Yang-Mills systems and show that the underlying symmetry is a supersymmetric generalization of BMS symmetry. We construct…
Using a duality between the space of particles and the space of fields, we show how one can compute form factors directly in the space of fields. This introduces the notion of vertex operators, and form factors are vacuum expectation values…
A possible quantum-mechanical origin of statistical mechanics is discussed, and microcanonical and canonical ensembles of bosons and fermions are derived from the stationary Schr\"odinger equation in a unified manner. The interaction…
Considering a fluctuating scalar field on momentum space, some relativistic statistical field theories are constructed. A Hilbert space of observables is then constructed from functionals of the fluctuating scalar field with an inner…
Composite fermions provide a simple and unified picture to understand a vast amount of phenomenology in the quantum Hall regime. However it has remained challenging to formulate this concept properly within a single Landau level. Recently a…
We study the consistency of having Lorentz invariance as a low energy approximation within the quantum field theory framework. A model with a scalar and a fermion field is used to show how a Lorentz invariance violating high momentum scale,…
The anti self-adjoint operators of imaginary coordinate and momentum, together with the self-adjoint operators of real coordinate, momentum, energy and time are used in construction of the quantum field theory in operator form. This…
Algebras associated with Quantum Electrodynamics and other gauge theories share some mathematical features with T-duality Exploiting this different perspective and some category theory, the full algebra of fermions and bosons can be…
In this paper we study the charged electro-weak interactions in the de Sitter geometry. We develop the reduction formalism for the Proca field with the help of the solutions for the interacting fields. Perturbation theory is used for…
Exotic topologically protected zero modes with parafermionic statistics (also called fractionalized Majorana modes) have been proposed to emerge in devices fabricated from a fractional quantum Hall system and a superconductor. The…
Recently a new bosonization method has been used to derive, at zero fermion density, an effective action for relativistic field theories whose partition function is dominated by fermionic composites, chiral mesons in the case of QCD. This…
We demonstrate that the rapidity and robustness of slow contraction in homogenizing and flattening the universe found in simulations in which the initial conditions were restricted to non-perturbative variations described by a single…
In several self-coupled quantum field theories when treated in semi-classical limit one obtains solitonic solutions determined by topology of the boundary conditions. Such solutions, e.g. magnetic monopole in unified theories…
We construct finite Dyson boson-fermion mappings of general collective algebras extended by single-fermion operators. A key element in the construction is the implementation of a similarity transformation which transforms boson-fermion…
We present field theoretical descriptions of massless (2+1) dimensional nonrelativistic fermions in an external magnetic field, in terms of a fermionic and bosonic second quantized language. An infinite dimensional algebra, $W_{\infty}$,…