Related papers: Quantization of systems with $OSp(2|2)$ symmetry
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
The quantization of systems with first- and second-class constraints within the coherent-state path-integral approach is extended to quantum systems with fermionic degrees of freedom. As in the bosonic case the importance of path-integral…
Under the principle that quantum mechanical observables are invariant under relevant symmetry transformations, we explore how the usual, non-invariant quantities may capture measurement statistics. Using a relativisation mapping, viewed as…
We propose a very simple toy model of a $\mathbb{Z}_2^2$-supersymmetric quantum system and show, via Klein's construction, how to understand the system as being an $N=2$ supersymmetric system with an extra $\mathbb{Z}_2^2$-grading. That is,…
We discuss two different nonlinear generalizations of the osp(2|2) supersymmetry which arise in superconformal mechanics and fermion-monopole models.
We report briefly on an approach to quantum theory entirely based on symmetry grounds which improves Geometric Quantization in some respects and provides an alternative to the canonical framework. The present scheme, being typically…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
Ordered chains (such as chains of amino acids) are ubiquitous in biological cells, and these chains perform specific functions contingent on the sequence of their components. Using the existence and general properties of such sequences as a…
We propose a superfield description of osp(1,2) covariant quantization by extending the set of admissibility conditions for the quantum action. We realize a superfield form of the generating equations, specify the vacuum functional and…
New measures for the quantization of systems with constraints are discussed and applied to several examples, in particular, examples of alternative but equivalent formulations of given first-class constraints, as well as a comparison of…
In manifolds with spatial boundary, BRST formalism can be used to quantize gauge theories. We show that, in a $U(1)$ gauge theory, only a subset of all the boundary conditions allowed by the self-adjointness of the Hamiltonian preserves…
The quantization of a massive spin $1/2$ field that satisfies the Klein-Gordon equation is studied. The framework is consistent, provided it is formulated as a pseudo-hermitian quantum field theory by the redefinition of the field dual and…
The relativistic 20-component wave equation, describing particles with spin 1/2 and two mass states, is analyzed. The projection operators extracting states with definite energy and spin projections, and density matrix are obtained. The…
We reexamine the connection between spin and statistics through the quantization of a complex scalar field, using the formulation with the property that the hermitian conjugate of canonical momentum for a variable is just the canonical…
Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of…
The structure of state vector space for a general (non-anomalous) gauge theory is studied within the Lagrangian version of the $Sp(2)$-symmetric quantization method. The physical {\it S}-matrix unitarity conditions are formulated. The…
The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of…
General dynamic properties like controllability and simulability of spin systems, fermionic and bosonic systems are investigated in terms of symmetry. Symmetries may be due to the interaction topology or due to the structure and…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
The aim of this lecture is to present in a comprehensible way what the BRST quantization means and how the "classical" master equation, action and BRST transformations have to be prolonged towards the same "quantum" items. The presentation…