Related papers: Quantization of multidimensional variational princ…
We develop a mathematical theory of quantization of multidimensional variational principles, and compare it with traditional constructions of quantum field theory. We conjecture that mathematical realization of quantum field theory axioms,…
We give a mathematical definition of quantum field theory on a manifold, and definition of quantization of a classical field theory given by a variational principle.
We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric…
A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of…
The role of symmetries in formation of quantum dynamics is discussed. A quantum version of the d'Alambert's principle is proposed to take into account symmetry constrains for quantum case. It is noted that in this approach one can find, in…
The review paper presents generalization of d'Alembert's variational principle: the dynamics of a quantum system for an external observer is defined by the exact equilibrium of all acting in the system forces, including the random quantum…
D-theory is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantized variables instead of classical fields. Classical scalar fields are replaced by generalized quantum spins and classical…
We construct a quantum theory of free scalar field in 1+1 dimensions based on a `Generalized Uncertainty Principle'. Both canonical and path integral formalism are employed. Higher dimensional extension is easily performed in the path…
The aim of the note is to provide an introduction to the algebraic, geometric and quantum field theoretic ideas that lie behind the Kontsevich-Cattaneo-Felder formula for the quantization of Poisson structures. We show how the quantization…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…
The gauge invariant observables of the closed bosonic string are quantized without anomalies in four space-time dimensions by constructing their quantum algebra in a manifestly covariant approach. The quantum algebra is the kernel of a…
A concise discussion of a 3+1-dimensional derivative coupling model, in which a massive Dirac field couples to the four-gradient of a massless scalar field, is given in order to elucidate the role of different concepts in quantum field…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
We construct the commutative Poisson algebra of classical Hamiltonians in field theory. We pose the problem of quantization of this Poisson algebra. We also make some interesting computations in the known quadratic part of the quantum…
The "quantum duality principle" states that the quantization of a Lie bialgebra - via a quantum universal enveloping algebra (QUEA) - provides also a quantization of the dual Lie bialgebra (through its associated formal Poisson group) - via…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
A theoretical study is made of conformal factors in certain types of physical theories based on classical differential geometry. Analysis of quantum versions of Weyl's theory suggest that similar field equations should be available in four,…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
There exists the problem to construct a quantum algebra of observables in lightcone QCD beyond the perturbative regime. It has recently established that the boundary gauge fields are crucial for a consistent construction of the classical…
We explain that a bulk with arbitrary dimensions can be added to the space over which a quantum field theory is defined. This gives a TQFT such that its correlation functions in a slice are the same as those of the original quantum field…