Classical nonrelativistic effective field theories for a real scalar field
A classical nonrelativistic effective field theory for a real Lorentz-scalar field $$\phi$$ is most conveniently formulated in terms of a complex scalar field $$\psi$$. There have been two derivations of effective Lagrangians for the complex field $$\psi$$ in which terms in the effective potential were determined to order $$(\psi^* \psi)^4$$. We point out an error in each of the effective Lagrangians. After correcting the errors, we demonstrate the equivalence of the two effective Lagrangians by verifying that they both reproduce $$T$$-matrix elements of the relativistic real scalar field theory and by also constructing a redefinition of the complex field $$\psi$$ that transforms terms in one effective Lagrangian into the corresponding terms of the other.
- Research Organization:
- The Ohio State Univ., Columbus, OH (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)
- Grant/Contract Number:
- SC0011726; PHY-1310862
- OSTI ID:
- 1482766
- Alternate ID(s):
- OSTI ID: 1602490
- Journal Information:
- Physical Review. D., Journal Name: Physical Review. D. Vol. 98 Journal Issue: 9; ISSN 2470-0010
- Publisher:
- American Physical Society (APS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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