Related papers: Quantization of Nambu Brackets from Operator Forma…
A Local Resolution of the Problem of Time has recently been given, alongside reformulation as A Local Theory of Background Independence. The classical part of this can be viewed as requiring just Lie's Mathematics, albeit entrenched in…
In Hamiltonian mechanics, a (continuous) symmetry leads to conserved quantity, which is a function on (extended) phase space. In Nambu mechanics, a straightforward consequence of symmetry is just a relative integral invariant, a…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
I consider an algebraic construction of creation and annihilation operators for superstring and p-brane parton models. The result can be interpreted as a realisation of multiple quantisation and suggests a relationship between quantisation…
We consider deformations of CFTs from the perspective of parallel transport in moduli space. In particular, we show how the deformations of individual operators can be computed and we also explore how these ideas can be extended to more…
We generalize an identity, first found by Bremner, for the action of three nested Nambu brackets.
T-duality is one of the essential elements of string theory. Recently, Hull has developed a formalism where the dimension of the target space is doubled so as to make T-duality manifest. This is then supplemented with a constraint equation…
We review an approach towards a covariant formulation of Matrix theory based on a discretization of the 11d membrane. Higher dimensional algebraic structures, such as the quantum triple Nambu bracket, naturally appear in this approach. We…
The new method based on the operator formalism proposed by Abe and Nakanishi is applied to the quantum nonlinear abelian gauge theory in two dimension. The soluble models in this method are extended to wider class of quantum field theories.…
We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges and…
Using a fully covariant formalism given by Carter for the deformation dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved background, it is proved that the corresponding Witten's phase space is endowed with a covariant…
In this article we present bosonic T-dualization in double space of the type II superstring theory in pure spinor formulation. We use the action with constant background fields obtained from the general case under some physically and…
We propose a way to identify the gauge invariant operator in noncommutative gauge theory on a D-brane with nonzero B field which couples to a specific supergravity mode in the bulk. This uses the description of noncommutative gauge theories…
We present a duality procedure that relates conventional four-dimensional matter-coupled N=1 supergravities to dual formulations in which auxiliary fields are replaced by field-strengths of gauge three-forms. The duality promotes specific…
Following a suggestion by Vafa, we present a quantum-mechanical model for S-duality symmetries observed in the quantum theories of fields, strings and branes. Our formalism may be understood as the topological limit of Berezin's metric…
Recent formal solutions of BRST quantization on inner product spaces within the operator method are shown to lead to an unexpected interpretation of the conventional path integral formulation. The relation between the Hamiltonians in the…
The quantization problem for the trace-bracket algebra, derived from double Poisson brackets, is discussed. We obtain a generalization of the boundary YBE (or so-called ABCD-algebra) for the quantization of quadratic trace-brackets. A…
The dynamic of a classical system can be expressed by means of Poisson brackets. In this paper we generalize the relation between the usual non covariant Hamiltonian and the Poisson brackets to a covariant Hamiltonian and new brackets in…
Quantization is still a central problem of modern physics. One example of an unsolved problem is the quantization of Nambu mechanics. After a brief comment on the role of Harrison cohomology, this review concentrates on the central problem…
Several quantum gravity and string theory thought experiments indicate that the Heisenberg uncertainty relations get modified at the Planck scale so that a minimal length do arises. This modification may imply a modification of the…