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A systematic way of formulating the Batalin-Vilkovisky method of quantization was obtained in terms of the ``odd time formulation. We show that in a class of gauge theories it is possible to find an ``odd time lagrangian yielding, by a Legendre transformation, an ``odd time hamiltonian which is the minimal solution of the master equation. This constitutes a very simple method of finding the minimal solution of the master equation which is usually a tedious task. To clarify the general procedure we discussed its application to Yang-Mills theory, massive (abelian) theory in Stueckelberg formalism, relativistic particle and the self-interacting antisymmetric tensor field.
A lack of regularity in the solution of the porous medium equation poses a serious challenge in its theoretical and numerical studies. A common strategy in theoretical studies is to utilize the pressure formulation of the equation where a new variabl
The bosonic large-$N$ master field of the IIB matrix model can, in principle, give rise to an emergent classical spacetime. The task is then to calculate this master field as a solution of the bosonic master-field equation. We consider a simplified v
It has been argued that the bosonic large-$N$ master field of the IIB matrix model can give rise to an emergent classical spacetime. In a recent paper, we have obtained solutions of a simplified bosonic master-field equation from a related matrix mod
We consider Yukawa theory in which the fermion mass is induced by a Higgs like scalar. In our model the fermion mass exhibits a temporal dependence, which naturally occurs in the early Universe setting. Assuming that the complex fermion mass changes
One of the useful and practical methods for solving quantum-mechanical many-body systems is to recast the full problem into a form of the effective interaction acting within a model space of tractable size. Many of the effective-interaction theories