Seminars: D. G. Levkov, Exact High-Multiplicity Amplitudes from Landau Method

SEMINARS


Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS February 11, 2026 14:00, Moscow, Steklov Mathematical Institute of RAS, Room 313 (8 Gubkina)

Exact High-Multiplicity Amplitudes from Landau Method D. G. Levkov^ab ^a Institute for Nuclear Research, Russian Academy of Sciences, Moscow ^b Institute for Theoretical and Mathematical Physics of Lomonosov Moscow State University
Abstract: We propose a new perturbatively exact relation between $n$-point amplitudes in bosonic theories and vacuum-to-vacuum transition amplitudes in the same theories with vanishingly weak sources on singular backgrounds. Derivation of this relation is based on exact version of semiclassical Landau method for calculating matrix elements. We show that the new formula resums the powers of $gn$ in the perturbative series and thus describes double-scaling limits $g \to 0$, $gn=\mathrm{const}$ of $n$-particle production amplitude in $g\phi^4$ theory and of vacuum-to-n-th excited state transition amplitude in quantum mechanics with semiclassical parameter g. In the leading semiclassical order, our approach substantiates D. T. Son's method of singular solutions and Rubakov-Son-Tinyakov conjecture on universality of semiclassical exponent. We illustrate the new method in the model of quantum anharmonic oscillator and apply it to $(3+1)$- dimensional $g\phi^4$ theory. The talk is based on joint work with S. V. Demidov (INR RAS & MIPT & MSU) and B. R. Farkhtdinov (INR RAS & Sechenov U.).