Symplectic field theory and quantum backgrounds

Symplectic Field Theory and Quantum Backgrounds

We derive an L∞ structure associated to a polarized quantum background and characterize the obstructions to finding a versal solution to the quantum master equation (QME). We illustrate how symplectic field theory (SFT) is an example of a polarized quantum background and discuss the L∞ structure in the SFT context. The discussion may be summarized as follows: given a contact manifold M with con...

Quantum Field Theory on Curved Backgrounds

Quantum Field Theory - Quantum String Duality in Curved Backgrounds

We introduce a R “Dual” transform which relates Quantum Field Theory and Quantum String regimes, both in a curved background. This operation maps the characteristic len gth of one regime into the other and, as a consequence, mass domains as well. The Hawking-Gibbons tempe rature and the string maximal or critical temperature are dual of each other. If back reaction of quan tum matter is include...

Quantum Field Theory on Curved Backgrounds. II. Spacetime Symmetries

We study space-time symmetries in scalar quantum field theory on an arbitrary static space-time. We first consider Euclidean quantum field theory, and show that the isometry group is generated by one-parameter subgroups which have either selfadjoint or unitary quantizations. We then show that the self-adjoint semigroups thus constructed can be analytically continued to one-parameter unitary gro...

Magnetic Backgrounds and Noncommutative Field Theory

• Introduction • Strong Magnetic Fields (a) The Landau problem (b) The lowest Landau level (c) Field theory • String Theory and D-Branes (a) Noncommutative geometry in string theory (b) D-branes (c) String theory in magnetic fields • Noncommutative Quantum Field Theory (a) Fundamental aspects (b) UV/IR mixing (c) Gauge interactions (d) Violations of special relativity • The Fractional Quantum H...