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We use the General Boundary Formulation (GBF) of Quantum Field Theory to compute the S-matrix for a general interacting scalar field in a wide class of curved spacetimes. As a by-product we obtain the general expression of the Feynman…
Quantum field theory in the $4$-dimensional de Sitter space-time is constructed in the ambient space formalism in a rigorous mathematical framework. This work is based on the group representation theory and the analyticity of the…
The worldline casting of a gauge field system with spin-1/2 matter fields has provided a, particle-based, first quantization formalism in the framework of which the Bern-Kosower algorithms for efficient computations in QCD acquire a simple…
The vector system of linear differential equations for a field with arbitrary fractional spin is proposed using infinite-dimensional half-bounded unitary representations of the $\overline{SL(2,R)}$ group. In the case of $(2j+1)$-dimensional…
Phase-space representations as given by Wigner functions are a powerful tool for representing the quantum state and characterizing its time evolution in the case of infinite-dimensional quantum systems and have been widely used in quantum…
A general method to construct free quantum fields for massive particles of arbitrary definite spin in a canonical Hamiltonian framework is presented. The main idea of the method is as follows: a multicomponent Klein-Gordon field that…
We present a general theory of mixing for an arbitrary number of fields with integer or half-integer spin. The time dynamics of the interacting fields is solved and the Fock space for interacting fields is explicitly constructed. The…
All elementary particles in nature can be classified as fermions with half-integer spin and bosons with integer spin. Within quantum electrodynamics (QED), even though the spin of the Dirac particle is well defined, there exist open…
We develop a rigorous framework for constructing Fock representations of quantum fields obeying generalized statistics associated with certain solutions of the spectral quantum Yang-Baxter equation. The main features of these…
We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive…
In this paper we elaborate on the gauge invariant frame-like Lagrangian description for the wide class of the so-called infinite (or continuous) spin representations of Poincar\'e group. We use our previous results on the gauge invariant…
Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the…
These lectures discuss the formulation of quantum mechanics with fractional spin and statistics in 2+1 dimensions in a relativistic setting, emphasizing the path-integral approach. The non-relativistic theory is reviewed from a…
We have treated numerous illustrative examples of spin relaxation problems using Wigner's phase-space formulation of quantum mechanics of particles and spins. The merit of the phase space formalism as applied to spin relaxation problems is…
We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…
In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with infinite number of degrees of freedom on compact base…
We construct local and global metaplectic double covers of odd general spin groups, using the cover of Matsumoto of spin groups. Following Kazhdan and Patterson, a local exceptional representation is the unique irreducible quotient of a…
We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this…
We present the complete first order relativistic quantum kinetic theory with spin for massive fermions derived from the Wigner function formalism in a concise form that shows explicitly how the 32 Wigner equations reduce to 4 independent…
We present a simple group representation analysis of massive, and particularly ``partially massless'', fields of arbitrary spin in de Sitter spaces of any dimension. The method uses bulk to boundary propagators to relate these fields to…