Related papers: QFT method for indefinite Kac-Moody Theory: A step…
Consider a d-dimensional quantum field theory (QFT) $\mathfrak{T}$, with a generalized symmetry $\mathcal{S}$, which may or may not be invertible. We study the action of $\mathcal{S}$ on generalized or $q$-charges, i.e. $q$-dimensional…
Recently it was shown that an asymptotic behaviour of $SU(N)$ gauge theory for large $N$ is described by q-deformed quantum field. The master fields for large N theories satisfy to standard equations of relativistic field theory but fields…
A quantum group analysis is applied to the Sine-Gordon model (or may be its version) in a strong-coupling regime. Infinitely many bound states are found together with the corresponding S-matrices. These new solutions of the Yang-Baxter…
Present day quantum field theory (QFT) is founded on canonical quantization, which has served quite well, but also has led to several issues. The free field describing a free particle (with no interaction term) can suddenly become…
We define a (3+1)-TQFT associated with possibly non-semisimple finite unimodular ribbon tensor categories using skein theory. This gives an explicit realization of a TQFT predicted by the cobordism hypothesis, based on recent results on…
The standard way to do computations in Quantum Field Theory (QFT) often results in the requirement of dramatic cancellations between contributions induced by a "heavy" sector into the physical observables of the "light" (or low energy)…
In [arXiv:1912.02063], we constructed 3-dimensional Topological Quantum Field Theories (TQFTs) using not necessarily semisimple modular categories. Here, we study projective representations of mapping class groups of surfaces defined by…
We study 2+1 dimensional gauge theories with a Chern-Simons term and a fermion in the adjoint representation. We apply general considerations of symmetries, anomalies, and renormalization group flows to determine the possible phases of the…
String-localized QFT allows to explain Standard Model interactions in an autonomous way, committed to quantum principles rather than a "gauge principle", thus avoiding an indefinite state space and compensating ghosts. The resulting…
We give a very brief introduction to the group field theory approach to quantum gravity, a generalisation of matrix models for 2-dimensional quantum gravity to higher dimension, that has emerged recently from research in spin foam models.
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
In this paper, we begin constructing a new finite-dimensional topological quantum field theory (TQFT) for three-manifolds, based on group PSL(2,C) and its action on a complex variable by fractional-linear transformations, by providing its…
We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, {\em Quantum Noise} (1991)]…
At long distances, a gapped phase of matter is described by a topological quantum field theory (TQFT). We conjecture a tight and concrete relationship between the genuine $(d+1)$-partite entanglement -- labelled by a $d$-dimensional…
We construct a new family of exact quantum field theories modeled on hyperbolic geometry, called {\it quantum hyperbolic field theories} (QHFTs). The QHFTs are defined for a $(2+1)$-bordism category based on the set of compact oriented…
We discuss some basic aspects of quantum fields on star graphs, focusing on boundary conditions, symmetries and scale invariance in particular. We investigate the four-fermion bulk interaction in detail. Using bosonization and vertex…
Quantum field theory is mostly known as the most advanced and well-developed theory in physics, which combines quantum mechanics and special relativity consistently. In this work, we study the spinless quantum field theory, namely the…
Today's quantum field theory (QFT) relies heavenly on canonical quantization (CQ), which fails for $\varphi^4_4$ leading only to a "free" result. Affine quantization (AQ), an alternative quantization procedure, leads to a "non-free" result…
Quantum field theory (QFT) based on the principles of special relativity (SR) and it is in fact the \emph{kinematic theory of fields}. The root assumption is that there is "relativistic description" of \emph{any} isolated quantum system in…
This note is an introduction to methods of construction for Hilbert space realizations of relativistic quantum physics. The realizations satisfy a revision to Wightman's functional analytic axioms and exhibit interaction in physical…