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We study various non-relativistic field theories with exotic symmetries called subsystem symmetries, which have recently attracted much attention in the context of fractons. We start with a scalar theory called $\phi$-theory in $d+1$…

Moving from the consideration that matter fields must be treated in terms of their fundamental quantum counterparts, we show straightforward arguments, within the framework of ordinary quantum mechanics and quantum field theory, in order to…

The mechanism underlying any bosonisation or fermionisation is exposed.It is shown that any local theory of fermions on a lattice in any spatial dimension greater than one is equivalent to a local theory of Ising spins coupled to a $Z_{2}$…

The Cartan's equations definig simple spinors (renamed pure by C. Chevalley) are interpreted as equations of motion in momentum spaces, in a constructive approach in which at each step the dimesions of spinor space are doubled while those…

The spin-base invariant formalism of Dirac fermions in curved space maintains the essential symmetries of general covariance as well as similarity transformations of the Clifford algebra. We emphasize the advantages of the spin-base…

Universal vector wave equations allowing for a unified description of anyons, and also of usual bosons and fermions in the plane are proposed. The existence of two essentially different types of anyons, based on unitary and also on…

Clifford algebras and Majorana conditions are analyzed in any spacetime. An index labeling inequivalent $\Gamma$-structures up to orthogonal conjugations is introduced. Inequivalent charge-operators in even-dimensions, invariant under Wick…

The Carroll algebra is constructed as the $c\to0$ limit of the Poincare algebra and is associated to symmetries on generic null surfaces. In this paper, we begin investigations of Carrollian fermions or fermions defined on generic null…

The falling charge puzzle in gravitational field is well known due to the discussions of radiation. The puzzle lies in the heart of linking the electromagnetism and gravity. Up to date few discussions have fully taken account of quantum…

The exploration of scalar field theories that exhibit Carroll and Galilei symmetries has attracted a lot of attention. In this paper, we generalize these studies to fermionic field theories and construct consistent electric and magnetic…

We show that the three-dimensional map between fermions and bosons at finite temperature generalises for all odd dimensions $d>3$. We further argue that such a map has a nontrivial large $d$ limit. Evidence comes from studying the gap…

A local supersymmetric action for a (2+1)-dimensional system including gravity, the electromagnetic field and a Dirac spin-1/2 field is presented. The action is a Chern-Simons form for a connection of the OSp(2|2) group. All the fields…

Seven commuting elements of the Clifford algebra $Cl_{7,7}$ define seven binary eigenvalues that distinguish the $2^7=128$ states of 32 fermions, and determine their parity, electric charge and interactions. Three commuting elements of the…

Given two parallelisms of a projective space we describe a construction, called blending, that yields a (possibly new) parallelism of this space. For a projective double space $(\mathbb{P},\parallel_\ell,\parallel_r)$ over a quaternion skew…

The approach unifying all the internal degrees of freedom - proposed by one of us - is offering a new way of understanding families of quarks and leptons. Spinors, namely, living in d(=1+13)-dimensional space, manifest in the observed…

Complex scalar fields charged under approximate $U(1)$ symmetries appear in well-motivated extensions of the Standard Model. One example is the field that contains the QCD axion field associated with the Peccei-Quinn symmetry; others…

We introduce a concept of an embedding of a quadratic space in an associative algebra. The general properties of such embeddings are analyzed by linking it to the Clifford algebra. Conversely, there isa simple description of the standard…

Quantum Gravity has been so elusive because we have tried to approach it by two paths which can never meet: standard quantum field theory and general relativity. The gateway is covariance under the complexified Clifford algebra of our…

We suggest model equations, which, from some point of view, describe local interaction of three physical fields: a field of matter, an electromagnetic field and a gravitational field. A base of the model is a field of matter described by…

We consider the response of a uniformly accelerated monopole detector that is coupled non-linearly to the nth power of a quantum scalar field in (D+1)-dimensional flat spacetime. We show that, when (D+1) is even, the response of the…