Related papers: Spin in the path integral: anti-commuting versus c…
We give background material and some details of calculations for two recent papers [1,2] where we derived a path integral representation of the transition element for supersymmetric and nonsupersymmetric nonlinear sigma models in one…
The general method introduced in a previous paperto build up a class of models invariant under generalization of Carroll and Galilei algebra is extended to systems including a set of Grassmann variables describing the spin degree of…
In this paper we continue the study of the path-integral formulation of classical mechanics and in particular we better clarify, with respect to previous papers, the geometrical meaning of the variables entering this formulation. With…
In nuclear and particle physics one is often faced with problems where perturbation theory is not applicable. An example of this is the description of bound states. Therefore, an exact solution of field theory to all orders is an…
The Jordan-Schwinger map is widely employed to switch between bosonic or fermionic mode operators and spin observables, with numerous applications ranging from quantum field theories of magnetism and ultracold quantum gases to quantum…
We consider classical and quantum mechanics related to an additional noncommutativity, symmetric in position and momentum coordinates. We show that such mechanical system can be transformed to the corresponding one which allows employment…
We study the path integral formulation of Friedmann universe filled with a massless scalar field in loop quantum cosmology. All the isotropic models of $k=0,+1,-1$ are considered. To construct the path integrals in the timeless framework, a…
The formulation of noncommutative quantum mechanics as a quantum system represented in the space of Hilbert-Schmidt operators is used to systematically derive, using the standard time slicing procedure, the path integral action for a…
We introduce a transformation which allows the fermionization of operators of any one-dimensional spin-chain. This fermionization procedure is independent of any eventual integrable structure and is compatible with it. We illustrate this…
The Grassmann representation for the system of qubits, is considered. The treatment is based on natural description of the qubits system as fermions and uses coherent states of fermions. The quantum logic gates are represented in two forms…
The derivation of the boson representation of spin operators is given which reproduces the Holstein-Primakoff and Dyson-Maleev transformations in the corresponding cases. The suggested formalism allows to address some subtle issues which…
I investigate bosonization in four dimensions, using the smooth bosonization scheme. I argue that generalized chiral ``phases'' of the fermion field corresponding to chiral phase rotations and ``chiral Poincare transformations'' are the…
We study quantum spin chains solvable via hidden free fermionic structures. We study the algebras behind such models, establishing connections to the mathematical literature of the so-called ``graph-Clifford'' or ``quasi-Clifford''…
A novel approach, the fermion-spin transformation to implement the charge-spin separation, is developed to study the low-dimensional $t$-$J$ model. In this approach, the charge and spin degrees of freedom of the physical electron are…
We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a…
A complete treatment of the (2,2) NSR string in flat (2+2) dimensional space-time is given, from the formal path integral over N=2 super Riemann surfaces to the computational recipe for amplitudes at any loop or gauge instanton number. We…
A real-time path integral for ultrasoft QCD is formulated. It exhibits a Feynman's influence functional. The statistical properties of the theory and the gauge symmetry are explicit. The correspondence is established with the alternative…
The spin of a free electron is stable but its position is not. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have shown that the Feynman \emph{position} path integral can be mathematically defined as a…
We introduce a symmetric Poisson bracket that allows us to describe anticommuting fields on a classical level in the same way as commuting fields, without the use of Grassmann variables. By means of a simple example, we show how the Dirac…
We consider the fermionization of a bosonic free theory characterized by the 3+1D scalar - tensor duality. This duality can be interpreted as the dimensional reduction, via a planar boundary, of the 4+1D topological BF theory. In this…