Related papers: Exterior Differential Systems for Field Theories
The ``exotic'' particle model associated with the two-parameter central extension of the planar Galilei group can be used to derive the ground states of the Fractional Quantum Hall Effect. Similar equations arise for a semiclassical Bloch…
We consider N Dirac fermions on a 4-dimensional Euclidean space with a quadratic interaction given by arbitrary external Clifford-valued fields. The divergence of the axial current satisfies on the classical level a relation that is…
Two-dimensional non-abelian quantum field models provide a useful laboratory for analytic and numerical investigations of quantum theories with gauge symmetry. They can exhibit various features, such as charge confinement, which are known…
We present a lagrangian formulation for recently-proposed supersymmetric Yang-Mills theory in twelve dimensions. The field content of our multiplet has an additional auxiliary vector field in the adjoint representation. The usual Yang-Mills…
The large difference between the Planck scale and the electroweak scale, known as the hierarchy problem, has been addressed in some models through the existence of extra spatial dimensions. A search for evidence of extra spatial dimensions…
A new representation of Lagrangians of 4D nonlinear electrodynamics is considered. In this new formulation, in parallel with the standard Maxwell field strength F, an auxiliary bispinor (tensor) field V is introduced. The gauge field…
We construct a pseudo-Lagrangian that is invariant under rigid $E_{11}$ and transforms as a density under $E_{11}$ generalised diffeomorphisms. The gauge-invariance requires the use of a section condition studied in previous work on…
We compute the massive gauge and scalar corrections to form factors in both the Sudakov and threshold regimes up to and including two-loop orders. The corrections are calculated for processes involving two external fermions and scalars in…
Exceptional Field Theory employs an extended spacetime to make supergravity fully covariant under the U-duality groups of M-theory. The 12-dimensional EFT associated to the group $SL(2)\times\mathbb{R}^+$ together with its action is…
The quantum electrodynamics in presence of background external fields is developed. Modern methods of local quantum physics allow to formulate the theory on arbitrarily strong possibly time-dependent external fields. Non-linear observables…
We describe a novel approach to dimensional reduction in classical field theory. Inspired by ideas from noncommutative geometry, we introduce extended algebras of differential forms over space-time, generalized exterior derivatives and…
We consider dynamics of the quartet of interacting cosmic substrata, which includes the dynamic aether, presented by the unit timelike vector field, the axionic dark matter, described by the pseudoscalar field, the spinor field associated…
The concept "Classical Electromagnetism" in the title of the paper here refers to a theory built on three foundations: relativity principles, the original Maxwell's equations, and the mathematics of exterior calculus. In this theory of…
We consider the application of finite element exterior calculus (FEEC) methods to a class of canonical Hamiltonian PDE systems involving differential forms. Solutions to these systems satisfy a local multisymplectic conservation law, which…
We describe higher-dimensional theories whose low-energy 4D descriptions contain larger gauge or global symmetry groups. As an example, we construct a Higgsless SU(2) x U(1) model of electroweak symmetry breaking. The 5D SU(2) gauge…
We investigate how exotic differential structures may reveal themselves in particle physics. The analysis is based on the A. Connes' construction of the standard model. It is shown that, if one of the copies of the spacetime manifold is…
Lagrange scalar densities which are concomitants of two scalar fields, a pseudo-Riemannian metric tensor, and their derivatives of arbitrary differential order are investigated in a space of four-dimensions. I construct the most general…
The non-linear nature of Yang-Mills theory presents a challenge for extracting exact classical solutions, which are useful for understanding non-perturbative vacuum structures. In this paper, an algebraic tensor ring decomposition framework…
The uniqueness theorems for general relativity and Yang-Mills theories can be circumvented by dropping the ubiquitous, yet often implicit, assumption that physical fields, such as the spacetime metric, are fundamental. The novel concept of…
Some aspects of the "exotic" particle, associated with the two-parameter central extension of the planar Galilei group are reviewed. A fundamental property is that it has non-commuting position coordinates. Other and generalized…