Scale symmetry of quantum solitons
The nonlinear {sigma} model Lagrangian for a rotating and vibrating quantum soliton expressed in terms of collective coordinates is shown to possess a symmetry under scale transformation of the chiral field. By utilizing this symmetry, an integro-differential equation determining the chiral angle is...
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| Veröffentlicht in: | Physical review. D, Particles and fields Particles and fields, 1991-11, Vol.44 (10), p.3249-3253 |
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| container_title | Physical review. D, Particles and fields |
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| creator | CHEPILKO, N. M FUJII, K KOBUSHKIN, P |
| description | The nonlinear {sigma} model Lagrangian for a rotating and vibrating quantum soliton expressed in terms of collective coordinates is shown to possess a symmetry under scale transformation of the chiral field. By utilizing this symmetry, an integro-differential equation determining the chiral angle is obtained. A consistency condition between this equation and the Schroedinger equation for the quantum soliton is discussed, and a relation between the total soliton energy and that related to rotation and vibration is obtained without solving the Schroedinger equation. In the limiting case of only a vibrating or a rotating soliton, the integro-differential equation is reduced to a differential one, and the chiral angle becomes independent of eigensolutions of the relevant Schroedinger equation. The effects of chiral-symmetry breaking due to the pion mass are also examined. |
| doi_str_mv | 10.1103/PhysRevD.44.3249 |
| format | Article |
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The effects of chiral-symmetry breaking due to the pion mass are also examined.</description><identifier>ISSN: 0556-2821</identifier><identifier>EISSN: 1089-4918</identifier><identifier>DOI: 10.1103/PhysRevD.44.3249</identifier><identifier>PMID: 10013780</identifier><identifier>CODEN: PRVDAQ</identifier><language>eng</language><publisher>Ridge, NY: American Physical Society</publisher><subject>661100 - Classical & Quantum Mechanics- (1992-) ; 662120 - General Theory of Particles & Fields- Symmetry, Conservation Laws, Currents & Their Properties- (1992-) ; BOSON-EXCHANGE MODELS ; BOSONS ; CHIRAL SYMMETRY ; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; Classical and quantum physics: mechanics and fields ; DIFFERENTIAL EQUATIONS ; ELEMENTARY PARTICLES ; ENERGY LEVELS ; EQUATIONS ; Exact sciences and technology ; EXCITED STATES ; FUNCTIONS ; HADRONS ; HAMILTONIANS ; LAGRANGIAN FUNCTION ; MATHEMATICAL MODELS ; MATHEMATICAL OPERATORS ; MATHEMATICAL SPACE ; MESONS ; MINKOWSKI SPACE ; NONLINEAR PROBLEMS ; NUCLEON-NUCLEON POTENTIAL ; PARTIAL DIFFERENTIAL EQUATIONS ; PARTICLE MODELS ; PERIPHERAL MODELS ; Physics ; PHYSICS OF ELEMENTARY PARTICLES AND FIELDS ; PIONS ; POTENTIALS ; PSEUDOSCALAR MESONS ; QUANTIZATION ; QUANTUM OPERATORS ; QUASI PARTICLES ; ROTATIONAL STATES ; SCHROEDINGER EQUATION ; SIGMA MODEL ; SKYRME POTENTIAL ; SOLITONS ; SPACE ; SYMMETRY ; SYMMETRY BREAKING ; VIBRATIONAL STATES ; WAVE EQUATIONS</subject><ispartof>Physical review. 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M</creatorcontrib><creatorcontrib>FUJII, K</creatorcontrib><creatorcontrib>KOBUSHKIN, P</creatorcontrib><title>Scale symmetry of quantum solitons</title><title>Physical review. D, Particles and fields</title><addtitle>Phys Rev D Part Fields</addtitle><description>The nonlinear {sigma} model Lagrangian for a rotating and vibrating quantum soliton expressed in terms of collective coordinates is shown to possess a symmetry under scale transformation of the chiral field. By utilizing this symmetry, an integro-differential equation determining the chiral angle is obtained. A consistency condition between this equation and the Schroedinger equation for the quantum soliton is discussed, and a relation between the total soliton energy and that related to rotation and vibration is obtained without solving the Schroedinger equation. In the limiting case of only a vibrating or a rotating soliton, the integro-differential equation is reduced to a differential one, and the chiral angle becomes independent of eigensolutions of the relevant Schroedinger equation. The effects of chiral-symmetry breaking due to the pion mass are also examined.</description><subject>661100 - Classical & Quantum Mechanics- (1992-)</subject><subject>662120 - General Theory of Particles & Fields- Symmetry, Conservation Laws, Currents & Their Properties- (1992-)</subject><subject>BOSON-EXCHANGE MODELS</subject><subject>BOSONS</subject><subject>CHIRAL SYMMETRY</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>Classical and quantum physics: mechanics and fields</subject><subject>DIFFERENTIAL EQUATIONS</subject><subject>ELEMENTARY PARTICLES</subject><subject>ENERGY LEVELS</subject><subject>EQUATIONS</subject><subject>Exact sciences and technology</subject><subject>EXCITED STATES</subject><subject>FUNCTIONS</subject><subject>HADRONS</subject><subject>HAMILTONIANS</subject><subject>LAGRANGIAN FUNCTION</subject><subject>MATHEMATICAL MODELS</subject><subject>MATHEMATICAL OPERATORS</subject><subject>MATHEMATICAL SPACE</subject><subject>MESONS</subject><subject>MINKOWSKI SPACE</subject><subject>NONLINEAR PROBLEMS</subject><subject>NUCLEON-NUCLEON POTENTIAL</subject><subject>PARTIAL DIFFERENTIAL EQUATIONS</subject><subject>PARTICLE MODELS</subject><subject>PERIPHERAL MODELS</subject><subject>Physics</subject><subject>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</subject><subject>PIONS</subject><subject>POTENTIALS</subject><subject>PSEUDOSCALAR MESONS</subject><subject>QUANTIZATION</subject><subject>QUANTUM OPERATORS</subject><subject>QUASI PARTICLES</subject><subject>ROTATIONAL STATES</subject><subject>SCHROEDINGER EQUATION</subject><subject>SIGMA MODEL</subject><subject>SKYRME POTENTIAL</subject><subject>SOLITONS</subject><subject>SPACE</subject><subject>SYMMETRY</subject><subject>SYMMETRY BREAKING</subject><subject>VIBRATIONAL STATES</subject><subject>WAVE EQUATIONS</subject><issn>0556-2821</issn><issn>1089-4918</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1991</creationdate><recordtype>article</recordtype><recordid>eNpNkEtLw0AUhQdRbK3uXUkRF25S7zwyySylPqGg-FgPk8mERpJMmzsR8u9NSRXv5my-c-B-hJxTWFAK_OZ13eOb-75bCLHgTKgDMqWQqkgomh6SKcSxjFjK6IScIH7BcEzyYzKhAJQnKUzJ5bs1lZtjX9cutP3cF_NtZ5rQ1XP0VRl8g6fkqDAVurN9zsjnw_3H8ilavTw-L29XkeUxD5EDRg1TVNhCpXlunQOVMJukHHgiBIUkd0WSqcIyqjLKYpZJCWAly3MFAzYjl-Oux1BqtGVwdm190zgbtAQeKykG6HqENq3fdg6Drku0rqpM43yHmqaxYpzJ4b8ZgRG1rUdsXaE3bVmbttcU9E6f_tWnhdA7fUPlYr_eZbXL_xVGXwNwtQcMDuKK1jS2xD9OcJAqVfwHIW12zg</recordid><startdate>19911115</startdate><enddate>19911115</enddate><creator>CHEPILKO, N. M</creator><creator>FUJII, K</creator><creator>KOBUSHKIN, P</creator><general>American Physical Society</general><scope>IQODW</scope><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7X8</scope><scope>OTOTI</scope></search><sort><creationdate>19911115</creationdate><title>Scale symmetry of quantum solitons</title><author>CHEPILKO, N. M ; FUJII, K ; KOBUSHKIN, P</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c353t-e021a2914cf98ddcee0972c78303744107def7b9fc219b1252b6600c62dd90783</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1991</creationdate><topic>661100 - Classical & Quantum Mechanics- (1992-)</topic><topic>662120 - General Theory of Particles & Fields- Symmetry, Conservation Laws, Currents & Their Properties- (1992-)</topic><topic>BOSON-EXCHANGE MODELS</topic><topic>BOSONS</topic><topic>CHIRAL SYMMETRY</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>Classical and quantum physics: mechanics and fields</topic><topic>DIFFERENTIAL EQUATIONS</topic><topic>ELEMENTARY PARTICLES</topic><topic>ENERGY LEVELS</topic><topic>EQUATIONS</topic><topic>Exact sciences and technology</topic><topic>EXCITED STATES</topic><topic>FUNCTIONS</topic><topic>HADRONS</topic><topic>HAMILTONIANS</topic><topic>LAGRANGIAN FUNCTION</topic><topic>MATHEMATICAL MODELS</topic><topic>MATHEMATICAL OPERATORS</topic><topic>MATHEMATICAL SPACE</topic><topic>MESONS</topic><topic>MINKOWSKI SPACE</topic><topic>NONLINEAR PROBLEMS</topic><topic>NUCLEON-NUCLEON POTENTIAL</topic><topic>PARTIAL DIFFERENTIAL EQUATIONS</topic><topic>PARTICLE MODELS</topic><topic>PERIPHERAL MODELS</topic><topic>Physics</topic><topic>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</topic><topic>PIONS</topic><topic>POTENTIALS</topic><topic>PSEUDOSCALAR MESONS</topic><topic>QUANTIZATION</topic><topic>QUANTUM OPERATORS</topic><topic>QUASI PARTICLES</topic><topic>ROTATIONAL STATES</topic><topic>SCHROEDINGER EQUATION</topic><topic>SIGMA MODEL</topic><topic>SKYRME POTENTIAL</topic><topic>SOLITONS</topic><topic>SPACE</topic><topic>SYMMETRY</topic><topic>SYMMETRY BREAKING</topic><topic>VIBRATIONAL STATES</topic><topic>WAVE EQUATIONS</topic><toplevel>online_resources</toplevel><creatorcontrib>CHEPILKO, N. M</creatorcontrib><creatorcontrib>FUJII, K</creatorcontrib><creatorcontrib>KOBUSHKIN, P</creatorcontrib><collection>Pascal-Francis</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>MEDLINE - Academic</collection><collection>OSTI.GOV</collection><jtitle>Physical review. D, Particles and fields</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>CHEPILKO, N. M</au><au>FUJII, K</au><au>KOBUSHKIN, P</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Scale symmetry of quantum solitons</atitle><jtitle>Physical review. D, Particles and fields</jtitle><addtitle>Phys Rev D Part Fields</addtitle><date>1991-11-15</date><risdate>1991</risdate><volume>44</volume><issue>10</issue><spage>3249</spage><epage>3253</epage><pages>3249-3253</pages><issn>0556-2821</issn><eissn>1089-4918</eissn><coden>PRVDAQ</coden><abstract>The nonlinear {sigma} model Lagrangian for a rotating and vibrating quantum soliton expressed in terms of collective coordinates is shown to possess a symmetry under scale transformation of the chiral field. By utilizing this symmetry, an integro-differential equation determining the chiral angle is obtained. A consistency condition between this equation and the Schroedinger equation for the quantum soliton is discussed, and a relation between the total soliton energy and that related to rotation and vibration is obtained without solving the Schroedinger equation. In the limiting case of only a vibrating or a rotating soliton, the integro-differential equation is reduced to a differential one, and the chiral angle becomes independent of eigensolutions of the relevant Schroedinger equation. The effects of chiral-symmetry breaking due to the pion mass are also examined.</abstract><cop>Ridge, NY</cop><pub>American Physical Society</pub><pmid>10013780</pmid><doi>10.1103/PhysRevD.44.3249</doi><tpages>5</tpages></addata></record> |
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| identifier | ISSN: 0556-2821 |
| ispartof | Physical review. D, Particles and fields, 1991-11, Vol.44 (10), p.3249-3253 |
| issn | 0556-2821 1089-4918 |
| language | eng |
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| source | American Physical Society Journals |
| subjects | 661100 - Classical & Quantum Mechanics- (1992-) 662120 - General Theory of Particles & Fields- Symmetry, Conservation Laws, Currents & Their Properties- (1992-) BOSON-EXCHANGE MODELS BOSONS CHIRAL SYMMETRY CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Classical and quantum physics: mechanics and fields DIFFERENTIAL EQUATIONS ELEMENTARY PARTICLES ENERGY LEVELS EQUATIONS Exact sciences and technology EXCITED STATES FUNCTIONS HADRONS HAMILTONIANS LAGRANGIAN FUNCTION MATHEMATICAL MODELS MATHEMATICAL OPERATORS MATHEMATICAL SPACE MESONS MINKOWSKI SPACE NONLINEAR PROBLEMS NUCLEON-NUCLEON POTENTIAL PARTIAL DIFFERENTIAL EQUATIONS PARTICLE MODELS PERIPHERAL MODELS Physics PHYSICS OF ELEMENTARY PARTICLES AND FIELDS PIONS POTENTIALS PSEUDOSCALAR MESONS QUANTIZATION QUANTUM OPERATORS QUASI PARTICLES ROTATIONAL STATES SCHROEDINGER EQUATION SIGMA MODEL SKYRME POTENTIAL SOLITONS SPACE SYMMETRY SYMMETRY BREAKING VIBRATIONAL STATES WAVE EQUATIONS |
| title | Scale symmetry of quantum solitons |
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