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Concept
Differential Operator
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Concept
Elliptic Operator
An
elliptic operator
is a type of
differential operator
that generalizes the notion of a Laplacian and is characterized by its symbol being invertible everywhere except possibly at infinity. These operators are crucial in the study of
partial differential equations
as they often yield
well-posed problems
, leading to
smooth solutions
under appropriate
boundary conditions
.
Concept
Batalin-Vilkovisky Algebra
A
Batalin-Vilkovisky algebra
is a
graded commutative algebra
equipped with a
second-order differential operator
called the
BV operator
, which satisfies a specific
compatibility condition
with the
algebra's product
. It plays a crucial role in the
mathematical formulation
of
gauge theories
and quantization, particularly in the context of the
Batalin-Vilkovisky formalism
for
handling systems with symmetries
.
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