TY - JOUR

T1 - Towards a quantum theory of solitons

AU - Dvali, Gia

AU - Gomez, Cesar

AU - Gruending, Lukas

AU - Rug, Tehseen

N1 - Funding Information:
We thank Oscar Cata, Daniel Flassig, Slava Mukhanov and Ivo Sachs for useful discussions. The work of G.D. was supported in part by Humboldt Foundation under Humboldt Professorship, ERC Advanced Grant 339169 “Selfcompletion”, by TRR 33 “The Dark Universe” and by the DFG cluster of excellence “Origin and Structure of the Universe”. The work of C.G. was supported in part by Humboldt Foundation and by Grants: FPA 2009-07908 , CPAN ( CSD2007-00042 ) and by the ERC Advanced Grant 339169 “Selfcompletion”. The work of L.G. and T.R. was supported by the International Max Planck Research School on Elementary Particle Physics.
Publisher Copyright:
© 2015 The Authors.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the solitons can be understood from basic properties of quantum coherent states.

AB - We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the Noether charge of microscopic constituents gives rise to a topological charge in the macroscopic description. This fact explains the conservation of topological charge from the basic properties of coherent states. It also shows that no such conservation exists for non-topological solitons, which have finite mean occupation number. Consequently, they can have an exponentially-small but non-zero overlap with the vacuum, leading to vacuum instability. This amplitude can be interpreted as a coherent state description of false vacuum decay. Next we show that we can represent topological solitons as a convolution of two sectors that carry information about topology and energy separately, which makes their difference very transparent. Finally, we show how interaction among the solitons can be understood from basic properties of quantum coherent states.

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U2 - 10.1016/j.nuclphysb.2015.10.017

DO - 10.1016/j.nuclphysb.2015.10.017

M3 - Article

AN - SCOPUS:84946593770

SN - 0550-3213

VL - 901

SP - 338

EP - 353

JO - Nuclear Physics B

JF - Nuclear Physics B

ER -