In this paper we work out the explicit form of the change of variables that reproduces an arbitrary change of gauge in a higher-order Lagrangian formalism.
In the framework of $Sp(2)$ extended Lagrangian field-antifield BV formalism we study systematically the role of finite field-dependent BRST-BV transformations. We have proved that the Jacobian of a finite BRST-BV transformation is capable of generat
ing arbitrary finite change of the gauge-fixing function in the path integral.
We prove a double-inequality for the product of uncertainties for position and momentum of bound states for 1D quantum mechanical systems in the semiclassical limit.
We introduce external sources J_A directly into the quantum master action W of the field-antifield formalism instead of the effective action. The external sources J_A lead to a set of BRST-invariant functions W^A that are in antisymplectic involution
. As a byproduct, we encounter quasi--groups with open gauge algebras.
We introduce classical and quantum antifields in the reparametrization-invariant effective action, and derive a deformed classical master equation.
We provide necessary and sufficient conditions for a bi-Darboux Theorem on triplectic manifolds. Here triplectic manifolds are manifolds equipped with two compatible, jointly non-degenerate Poisson brackets with mutually involutive Casimirs, and with
ranks equal to 2/3 of the manifold dimension. By definition bi-Darboux coordinates are common Darboux coordinates for two Poisson brackets. We discuss both the Grassmann-even and the Grassmann-odd Poisson bracket case. Odd triplectic manifolds are, e.g., relevant for Sp(2)-symmetric field-antifield formulation. We demonstrate a one-to-one correspondence between triplectic manifolds and para-hypercomplex manifolds. Existence of bi-Darboux coordinates on the triplectic side of the correspondence translates into a flat Obata connection on the para-hypercomplex side.
We recalculate in a systematic and pedagogical way one of the most important results of Bosonic open string theory in the light-cone formulation, namely the [J^{-i},J^{-j}] commutators, which together with Lorentz covariance, famously yield the criti
cal dimension D=26 and the normal order constant a=1. We use traditional transverse oscillator mode expansions (avoiding the elegant but more advanced language of operator product expansions). We streamline the proof by introducing a novel bookkeeping/regularization parameter kappa to avoid splitting into creation and annihilation parts, and to avoid sandwiching between bras and kets.
It is well-known that the Fundamental Identity (FI) implies that Nambu brackets are decomposable, i.e., given by a determinantal formula. We find a weaker alternative to the FI that allows for non-decomposable Nambu brackets, but still yields a Darbo
ux-like Theorem via a Nambu-type generalization of Weinsteins splitting principle for Poisson manifolds.
We propose how to incorporate the Leites-Shchepochkina-Konstein-Tyutin deformed antibracket into the quantum field-antifield formalism.
We give an elementary proof of Noethers first Theorem while stressing the magical fact that the global quasi-symmetry only needs to hold for one fixed integration region. We provide sufficient conditions for gauging a global quasi-symmetry.
