Related papers: The Odd Fermion
We argue that having an odd number of Majorana fermion zero modes on a dynamical point-like soliton signifies an inconsistency in a theory with 3+1 and higher dimensions. We check this statement in a couple of examples in field theory and…
One of the interesting features about field theories in odd dimensions is the induction of parity violating terms and well-defined {\em finite} topological actions via quantum loops if a fermion mass term is originally present and…
We describe a possibility of creation of an odd number of fractionally charged fermions in 1+1 dimensional Abelian Higgs model. We point out that for 1+1 dimensions this process does not violate any symmetries of the theory, nor makes it…
The anomaly of a quantum field theory is an expression of its projective nature. This starting point quickly leads to its manifestation as a special kind of field theory: a once-categorified invertible theory. We arrive at this statement…
An effort is made to understand the phenomenological composite fermion model of the quantum Hall effect. The odd denominators are composed by adding plus minus 1 to the even numbers 2, 4, 6 and 8. Although the denominators are…
We give a modern geometric viewpoint on anomalies in quantum field theory and illustrate it in a 1-dimensional theory: supersymmetric quantum mechanics. This is background for the resolution of worldsheet anomalies in orientifold…
The phenomenon of quantum number fractionalization is explained. The relevance of non-trivial phonon field topology is emphasized.
The investigation of topological properties of the gauge field in a two-dimensional Higgs model can help in understanding anomalous fermion number violation.
We propose a supersymmetric quantum field theory with exotic symmetry related to fracton phases. We use superfield formalism and write down the action of a supersymmetric version of the $\varphi$ theory in 3+1 dimensions. It contains a…
In this paper, we construct a new topological quantum field theory of cohomological type and show that its partition function is a crossing number.
I construct a quantum field theory model with discrete scale invariance at tree level. The model has some unusual mathematical properties (such as the appearance of $q$-hypergeometric series) and may possibly have some interesting physical…
We study and explore the symmetry properties of fermions coupled to dynamical torsion and electromagnetic fields. The stability of the theory upon radiative corrections as well as the presence of anomalies are investigated.
We study the scattering of fermions off 't Hooft lines in the Standard Model. A long-standing paradox suggests that the outgoing fermions necessarily carry fractional quantum numbers. In a previous paper, we resolved this paradox in the…
We use the formalism of quantum off-shell fields for the case of pure Yang-Mills fields. In this formalism one can compute in a systematic way the second order anomalies of the tree sector.
In the context of quantum field theory, an anomaly exists when a theory has a classical symmetry which is not a symmetry of the quantum theory. This short exposition aims at introducing a new point of view, which is that the proper setting…
In loop quantum gravity the discrete nature of quantum geometry acts as a natural regulator for matter theories. Studies of quantum field theory in quantum space-times in spherical symmetry in the canonical approach have shown that the main…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
We develop a novel theoretical method for calculating spectroscopic properties of those nuclei with odd number of nucleons, that is based on the nuclear density functional theory and the particle-boson coupling scheme. Self-consistent…
Topology enters in quantum field theory (qft) in multiple forms: one of the most important, in non-abelian gauge theories, being in the identification of the $\theta$ vacuum in QCD. A very relevant aspect of this connection is through the…
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…