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The low energy effective action of gravity in any even dimension generally acquires non-local terms associated with the trace anomaly, generated by the quantum fluctuations of massless fields. The local auxiliary field description of this…
The structure of transition amplitudes in field theory in a three-dimensional space whose spatial coordinates are noncommutative and satisfy the SU(2) Lie algebra commutation relations is examined. In particular, the basic notions for…
The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…
An important methodological problem of theoretical mechanics related to inertia is discussed. Analysis Inertia is performed in four-dimensional Minkowski space-time based on the law of conservation of energy-momentum. This approach allows…
We examine the hypothesis that space-time is a product of a continuous four-dimensional manifold times a finite space. A new tensorial notation is developed to present the various constructs of noncommutative geometry. In particular, this…
The most general 2+1 dimensional spinning particle model is considered. The action functional may involve all the possible first order Poincare invariants of world lines, and the particular class of actions is specified thus the…
This work deals with braneworld scenarios driven by real scalar fields with standard dynamics. We show how the first-order formalism which exists in the case of four dimensional Minkowski space-time can be extended to de Sitter or anti-de…
A four dimensional scalar field theory with quartic and of higher power interactions suffers the triviality issue at the quantum level. This is due to coupling constants that, contrary to the physical expectations, seem to grow without a…
These notes comprise the second part of two articles devoted to the construction of exact solutions of noncommutative gauge theory in two spacetime dimensions. Here we shall deal with the quantum field theory. Topics covered include an…
The main principles of two-dimensional quantum field theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of…
It is natural to ask whether non-commutative geometry plays a role in four dimensional physics. By performing explicit computations in various toy models, we show that quantum effects lead to violations of Lorentz invariance at the level of…
We present a framework for discussing the cosmology of dark energy and dark matter based on two scalar degrees of freedom. An effective field theory of cosmological perturbations is employed. A unitary gauge choice renders the dark energy…
We study quantum field theories with boundary by utilizing non-invertible symmetries. We consider three kinds of boundary conditions of the four dimensional $\mathbb{Z}_2$ lattice gauge theory at the critical point as examples. The weights…
We study the problem of interacting theories with (partially)-massless and conformal higher spin fields without matter in three dimensions. A new class of theories that have partially-massless fields is found, which significantly extends…
I present a twistor action functional for null 2-surfaces (null strings) in 4D Minkowski spacetime. The proposed formulation is reparametrization invariant and free of algebraic and differential constraints. Proposed approach results in…
Starting from a theory of fermions moving in a fixed gauge and gravitational background we implement the scale invariance of the theory. Upon quantization the theory is anomalous but the anomaly can be cancelled by the addition of another…
A geometric interpretation of the spontaneous symmetry breaking effect, which plays a key role in the Standard Model, is developed. The advocated approach is related to the effective use of the momentum 4-spaces of the constant curvature,…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…
Gauge fields of mixed symmetry, corresponding to arbitrary representations of the local Lorentz group of the background spacetime, arise as massive modes in compactifications of superstring theories. We describe bosonic gauge field theories…
Recently, a gauge theory of unified gravity [Rep. Prog. Phys. 88, 057802 (2025)] has been developed to extend the Standard Model to include gravity. Here we present unified gravity using the ordinary four-vector and tensor field notation of…