Inner structure of Spin{sup c}(4) gauge potential on 4-dimensional manifolds
The decomposition of Spin{sup c}(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation {delta}A{sub {mu}}=-{lambda}A{sub {mu}} has been discovered. Here, {lambda} is the vacuum expectation value of the spinor field, {lambda}=-parallel {phi}-par...
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| Veröffentlicht in: | Annals of physics 2008-09, Vol.323 (9) |
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| container_title | Annals of physics |
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| creator | Liu Xin Duan Yishi Yang Wenli Institute of Modern Physics, Northwest University, Xian 710069 Zhang Yaozhong |
| description | The decomposition of Spin{sup c}(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation {delta}A{sub {mu}}=-{lambda}A{sub {mu}} has been discovered. Here, {lambda} is the vacuum expectation value of the spinor field, {lambda}=-parallel {phi}-parallel {sup 2}, and A{sub {mu}} the twisting U(1) potential. It is found that when {lambda} takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed. |
| doi_str_mv | 10.1016/j.aop.2008.06.002 |
| format | Article |
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Here, {lambda} is the vacuum expectation value of the spinor field, {lambda}=-parallel {phi}-parallel {sup 2}, and A{sub {mu}} the twisting U(1) potential. It is found that when {lambda} takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.</description><identifier>ISSN: 0003-4916</identifier><identifier>EISSN: 1096-035X</identifier><identifier>DOI: 10.1016/j.aop.2008.06.002</identifier><language>eng</language><publisher>United States</publisher><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; EIGENVALUES ; EQUATIONS ; EXPECTATION VALUE ; FOUR-DIMENSIONAL CALCULATIONS ; GAUGE INVARIANCE ; INSTANTONS ; LAPLACIAN ; MATHEMATICAL MANIFOLDS ; POTENTIALS ; SPIN ; SPINOR FIELDS ; TOPOLOGY ; U-1 GROUPS</subject><ispartof>Annals of physics, 2008-09, Vol.323 (9)</ispartof><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,780,784,885,27924,27925</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/21163730$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Liu Xin</creatorcontrib><creatorcontrib>Duan Yishi</creatorcontrib><creatorcontrib>Yang Wenli</creatorcontrib><creatorcontrib>Institute of Modern Physics, Northwest University, Xian 710069</creatorcontrib><creatorcontrib>Zhang Yaozhong</creatorcontrib><title>Inner structure of Spin{sup c}(4) gauge potential on 4-dimensional manifolds</title><title>Annals of physics</title><description>The decomposition of Spin{sup c}(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation {delta}A{sub {mu}}=-{lambda}A{sub {mu}} has been discovered. Here, {lambda} is the vacuum expectation value of the spinor field, {lambda}=-parallel {phi}-parallel {sup 2}, and A{sub {mu}} the twisting U(1) potential. It is found that when {lambda} takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. 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Here, {lambda} is the vacuum expectation value of the spinor field, {lambda}=-parallel {phi}-parallel {sup 2}, and A{sub {mu}} the twisting U(1) potential. It is found that when {lambda} takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.</abstract><cop>United States</cop><doi>10.1016/j.aop.2008.06.002</doi></addata></record> |
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| ispartof | Annals of physics, 2008-09, Vol.323 (9) |
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| subjects | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS EIGENVALUES EQUATIONS EXPECTATION VALUE FOUR-DIMENSIONAL CALCULATIONS GAUGE INVARIANCE INSTANTONS LAPLACIAN MATHEMATICAL MANIFOLDS POTENTIALS SPIN SPINOR FIELDS TOPOLOGY U-1 GROUPS |
| title | Inner structure of Spin{sup c}(4) gauge potential on 4-dimensional manifolds |
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