Three Natural Generalizations of Fedosov Quantization

Fedosov's simple geometrical construction for deformation quantization of symplectic manifolds is generalized in three ways without introducing new variables: (1) The base manifold is allowed to be a supermanifold. (2) The star product does not have to be of Weyl/symmetric or Wick/normal type. (3) The initial geometric structures are allowed to depend on Planck's constant.Comment: 21 pages, LaTeX. v2,v3,v4,v5: Minor changes, v6: References added, v7,v8: Minor changes, v9: Published versio

Path Integral Formulation with Deformed Antibracket

We propose how to incorporate the Leites-Shchepochkina-Konstein-Tyutin deformed antibracket into the quantum field-antifield formalism.Comment: 13 pages, LaTeX. v2: Added references. To appear in Phys. Lett.

Reparametrization-Invariant Effective Action in Field-Antifield Formalism

We introduce classical and quantum antifields in the reparametrization-invariant effective action, and derive a deformed classical master equation.Comment: 14 pages, LaTeX. v2: Further observations, Added one appendix. v3: Version submitted to IJMPA. v4: Version published in IJMP

Odd Scalar Curvature in Field-Antifield Formalism

We consider the possibility of adding a Grassmann-odd function \nu to the odd Laplacian. Requiring the total \Delta operator to be nilpotent leads to a differential condition for \nu, which is integrable. It turns out that the odd function \nu is not an independent geometric object, but is instead completely specified by the antisymplectic structure E and the density \rho. The main impact of introducing the \nu term is that it makes compatibility relations between E and \rho obsolete. We give a geometric interpretation of \nu as (minus 1/8 times) the odd scalar curvature of an arbitrary antisymplectic, torsion-free and \rho-compatible connection. We show that the total \Delta operator is a \rho-dressed version of Khudaverdian's \Delta_E operator, which takes semidensities to semidensities. We also show that the construction generalizes to the situation where \rho is replaced by a non-flat line bundle connection F. This generalization is implemented by breaking the nilpotency of \Delta with an arbitrary Grassmann-even second-order operator source.Comment: 23 pages, LaTeX. v2: More material added. v3: Reference added. v4: Grant number added. v5: Minor changes. v6: Stylistic change

Remarks on Existence of Proper Action for Reducible Gauge Theories

In the field-antifield formalism, we review existence and uniqueness proofs for the proper action in the reducible case. We give two new existence proofs based on two resolution degrees called "reduced antifield number" and "shifted antifield number", respectively. In particular, we show that for every choice of gauge generators and their higher stage counterparts, there exists a proper action that implements them at the quadratic order in the auxiliary variables.Comment: 37 pages, LaTeX. v2,v3: Minor corrections. v4: Added reference. To appear in IJMP

Symplectic Grassmannians, dual conformal symmetry and 4-point amplitudes in 6D

We investigate a new algebra-based approach of finding Grassmannian formulas for scattering amplitudes. Our prime motivation is massive amplitudes of 4D $\mathcal{N}=4$ SYM, and therefore we consider a 6D Grassmannian formula, where we can take advantage of massless kinematics. We next use symmetry arguments, and in particular, 6D dual conformal symmetry generalized to arbitrary dual conformal weights. Assuming a rational ansatz in terms of Pl\"{u}cker coordinates (i.e. minors) for the integrand, this approach leads to a set of algebraic equations. As an example, we explicitly find the solution for 4-point scattering amplitudes up to proportionality constants.Comment: 36 pages, LaTe