The semiclassical energy density of kinks and solitons

Abstract

We compute semiclassical corrections to the energy density of kinks in ${\varphi }^4$ theory and of solitons in the sine-Gordon model in $1+1$ dimensions, using local and covariant renormalization techniques from quantum field theory in curved spacetimes. For the semiclassical correction to the energy, we recover the known results. Our analysis highlights a subtlety in the definition of a conserved stress tensor for scalar field theories in $1+1$ dimension.

20 pages; Mathematica notebooks containing the relevant calculations as ancillary files; v3: final version

References in corpus (6)

• NLO Renormalization in the Hamiltonian Truncation
• Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• Kink-antikink scattering in a quantum vacuum
• The current density in quantum electrodynamics in external potentials
• One-loop results for kink and domain wall profiles at zero and finite temperature

Cited by in corpus (4)

• A Reduced Inner Product for Kink States
• One-Loop Quantum Stress-Energy Tensor for the Kink and sine-Gordon Solitons
• The Weyl anomaly in interacting quantum field theory on curved spacetimes
• Local operators in the Sine-Gordon model: ${\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ and the stress tensor