Related papers: The Master Field for QCD and $q$-Deformed Quantum …
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
The gauge field theories are usually quantized by fixing gauge. In this paper, we propose a new formalism that quantizes gauge fields without gauge fixing but naturally follows canonical formalism. New physical implications will follow.
We find an infinite dimensional free algebra which lives at large N in any SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural basis of this algebra is a free-algebraic generalization of Chebyshev polynomials and…
These lectures give an introduction to duality in Quantum Field Theory. We discuss the phases of gauge theories and the implications of the electric-magnetic duality transformation to describe the mechanism of confinement. We review the…
A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling…
We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather…
This extended write-up of a talk gives an introductory survey of mathematical problems of the quantization of gauge systems. Using the Schwinger model as an exactly tractable but nontrivial example which exhibits general features of gauge…
It is well known that a typical Yang-Mills Gauge Field is mediated by massless Bosons. It is only through a symmetry breaking mechanism, as in the Salam-Weinberg model that the quanta of such an interaction field acquire a mass in the usual…
Using the general notions of Batalin, Fradkin, Fradkina and Tyutin to convert second class systems into first class ones, we present a gauge invariant formulation of the massive Yang-Mills theory by embedding it in an extended phase space.…
Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…
A modular quantum architecture is given for the space-time, particles, and fields of the Standard Model and General Relativity. It assumes a right-handed neutrino, so that based on their multiplet structure all fundamental fermions have…
We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the…
The light-cone approach is reviewed. This method allows to find the underlying quantum field theory for any integrable lattice model in its gapless regime. The relativistic spectrum and S-matrix follows straightforwardly in this way through…
The massive non-Abelian gauge fields are quantized Lorentz-covariantly in the Hamiltonian path-integral formalism. In the quantization, the Lorentz condition, as a necessary constraint, is introduced initially and incorporated into the…
A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent…
The non commutative geometry is a possible framework to regularize Quantum Field Theory in a nonperturbative way. This idea is an extension of the lattice approximation by non commutativity that allows to preserve symmetries. The…
A gauge system is a classical field theory where among the fields there are connections in a principal G-bundle over the space-time manifold and the classical action is either invariant or transforms appropriately with respect to the action…
The large-charge master field which generates all n-point correlation functions with an insertion of large charge Q in non-relativistic conformal field theory is obtained. This field is used to compute Schr\"odinger-invariant n-point…
Lagragian quantization rules for general gauge theories are proposed on a basis of a superfield formulation of the standard BRST symmetry. Independence of the $S$-matrix on a choice of the gauge is proved. The Ward identities in terms of…