Pohlmeyer Charge

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experi ...

Pohlmeyer charge, named for Klaus Pohlmeyer, is a conserved charge invariant under the

Virasoro algebra In mathematics, the Virasoro algebra (named after the physicist Miguel Ángel Virasoro) is a complex Lie algebra and the unique central extension of the Witt algebra. It is widely used in two-dimensional conformal field theory and in string t ...

or its generalization. It can be obtained by expanding the holonomies (generating functions) :

P\,Tr\, \exp i T_\mu\oint d\sigma A_\sigma^(\sigma)

with respect to the constant matrices ''T''. The gauge field

A_\sigma^\mu

is defined as a combination of

\partial X^\mu

and its conjugate. According to the logic of

loop quantum gravity Loop quantum gravity (LQG) is a theory of quantum gravity, which aims to merge quantum mechanics and general relativity, incorporating matter of the Standard Model into the framework established for the pure quantum gravity case. It is an attem ...

and

algebraic quantum field theory Algebraic quantum field theory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic framework for quantum field theory, because it was introduced by . The axioms are stated in ter ...

, these charges are the right physical quantities that should be used for quantization. This logic is however incompatible with the standard and well-established methods of

quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...

based on

Fock space The Fock space is an algebraic construction used in quantum mechanics to construct the quantum states space of a variable or unknown number of identical particles from a single particle Hilbert space . It is named after V. A. Fock who first i ...

and

perturbation theory In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middl ...

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