Field redefinitions can be nonlocal

Cohen, Timothy [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Ecole Polytechnique Federale Lausanne (EPFL) (Switzerland); Univ. of Oregon, Eugene, OR (United States)] (ORCID:0000000270403038); Forslund, Matthew [Stony Brook Univ., NY (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States)] (ORCID:0000000301449339); Helset, Andreas [European Organization for Nuclear Research (CERN), Geneva (Switzerland)] (ORCID:0000000259043748)

doi:10.1007/jhep10(2025)019

DOE OSTI · 3008614

Field redefinitions can be nonlocal

Cohen, Timothy [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Ecole Polytechnique Federale Lausanne (EPFL) (Switzerland); Univ. of Oregon, Eugene, OR (United States)] (ORCID:0000000270403038)·Forslund, Matthew [Stony Brook Univ., NY (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States)] (ORCID:0000000301449339)·Helset, Andreas [European Organization for Nuclear Research (CERN), Geneva (Switzerland)] (ORCID:0000000259043748)

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Abstract

We revisit the lore establishing the allowed space of field redefinitions and show that there are essentially no restrictions. Our conclusions hold to all orders in perturbation theory and for any dispersion relation. Field redefinitions can be nonlocal, symmetry breaking, or in certain cases have explicit dependence on spacetime. We address field redefinitions that can be resummed into the propagator, which demonstrates how to perform perturbative calculations away from the minimum in field space. Field redefinitions are used to derive higher-order Schwinger-Dyson equations, which imply multiparticle soft theorems. Non-standard field redefinitions are showcased using both relativistic and nonrelativistic examples.

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Cohen, Timothy [European Organization for Nuclear Research (CERN), Geneva (Switzerland); Ecole Polytechnique Federale Lausanne (EPFL) (Switzerland); Univ. of Oregon, Eugene, OR (United States)] (ORCID:0000000270403038), Forslund, Matthew [Stony Brook Univ., NY (United States); Brookhaven National Laboratory (BNL), Upton, NY (United States)] (ORCID:0000000301449339), Helset, Andreas [European Organization for Nuclear Research (CERN), Geneva (Switzerland)] (ORCID:0000000259043748). 2025-10-02. Field redefinitions can be nonlocal. https://doi.org/10.1007/jhep10(2025)019

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