Related papers: Nonholonomic constraints in classical field theori…
The cosmological dynamics of multiple scalar/pseudoscalar fields are difficult to solve, especially when the field-space metric is curved. This presents a challenge in determining whether a given model can support cosmic acceleration,…
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…
For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential…
A novel algorithm is provided to couple a Galilean invariant model with curved spatial background by taking nonrelativistic limit of a unique minimally coupled relativistic theory, which ensures Galilean symmetry in the flat limit and…
We study the problem of imposing Dirichlet-like boundary conditions along a static spatial curve, in a planar Noncommutative Quantum Field Theory model. After constructing interaction terms that impose the boundary conditions, we discuss…
In contrast with QFT, classical field theory can be formulated in strict mathematical terms of fibre bundles, graded manifolds and jet manifolds. Second Noether theorems provide BRST extension of this classical field theory by means of…
The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic…
We study the real, massive Klein-Gordon field on a $C^\infty$ globally-hyperbolic background space-time with compact Cauchy hypersurfaces. In particular, the parametrization of this system as initiated by Dirac and Kucha\v{r} is put on a…
A novel way of defining limits in classical statistics is proposed. This is a natural extension of the original Neyman's method, and has the desirable property that only information relevant to the problem is used in making statistical…
With the covariant formulation in hand from the first paper of this series (physics/9801019), we begin in this second paper to study the canonical (or ``instantaneous'') formulation of classical field theories. The canonical formluation…
We demonstrate the usefulness of anholonomic frames in the contexts of nonholonomic and vakonomic systems. We take a consistently differential-geometric approach. As an application, we investigate the conditions under which the dynamics of…
The background dynamical evolution of a universe filled with matter and a cosmological scalar field is analyzed employing dynamical system techniques. After the phenomenology of a canonical scalar field with exponential potential is…
Using the skew-symmetry of the differential operators and multiplication operators in the canonical representations of finite-dimensional classical Lie algebras, we obtain some noncanonical polynomial representations of the classical Lie…
Multisymplectic geometry - which originates from the well known de Donder-Weyl theory - is a natural framework for the study of classical field theories. Recently, two algebraic structures have been put forward to encode a given theory…
The purpose of this paper is to show that, at least for Lagrangians of mechanical type, nonholonomic Euler-Lagrange equations for a nonholonomic linear constraint D may be viewed as non-constrained Euler-Lagrange equations but on a new…
A new form of quasiclassical space-time dynamics for constrained systems reveals how quantum effects can be derived systematically from canonical quantization of gravitational systems. These quasiclassical methods lead to additional fields,…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
New developments on the symmetries of non-relativistic field theoretical models on the non commutative plane are reviewed. It is shown in particular that Galilean invariance strongly restricts the admissible interactions. Moreover, if a…
In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on…
We propose a general definition of nonequilibrium entropy of a classical stochastic field. As an example of particular interest in cosmology we apply this definition to compute the entropy of density perturbations in an inflationary…