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 List of natural phenomena, natural phenomena. This is in contrast to experimental p ...

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

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

or its generalization. It can be obtained by expanding the holonomies (generating functions)Mikhailov, A. (2005)
Geometry of fast moving strings
:

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 that incorporates matter of the Standard Model into the framework established for the intrinsic quantum gravity case. It is an attempt to develop a quantum theory of gravity based direc ...

and algebraic quantum field theory, 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 Field theory (physics), field theory and the principle of relativity with ideas behind quantum mechanics. QFT is used in particle physics to construct phy ...

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 intro ...

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 middle ...

References

Quantum field theory Conformal field theory {{quantum-stub