On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills Thermodynamics
For a pure SU(2) Yang–Mills theory in 4D, we revisit the spatial (3D), ball-like region of radius <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mn>0</mn></msub>&l...
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MDPI AG
2022-02-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/8/2/117 |
| _version_ | 1797476207193751552 |
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| author | Ralf Hofmann Thierry Grandou |
| author_facet | Ralf Hofmann Thierry Grandou |
| author_sort | Ralf Hofmann |
| collection | DOAJ |
| description | For a pure SU(2) Yang–Mills theory in 4D, we revisit the spatial (3D), ball-like region of radius <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mn>0</mn></msub></semantics></math></inline-formula> in its bulk subject to the pressureless, deconfining phase at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mn>0</mn></msub><mo>=</mo><mn>1.32</mn><mspace width="0.166667em"></mspace><msub><mi>T</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula> denotes the critical temperature for the onset of the deconfining–preconfining phase transition. Such a region possesses finite energy density and represents the self-intersection of a figure-eight shaped center-vortex loop if a BPS monopole of core radius ∼<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfrac><msub><mi>r</mi><mn>0</mn></msub><mrow><mn>52.4</mn></mrow></mfrac></semantics></math></inline-formula>, isolated from its antimonopole by repulsion externally invoked through a transient shift of (anti)caloron holonomy (pair creation), is trapped therein. The entire soliton (vortex line plus region of self-intersection of mass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>m</mi><mn>0</mn></msub></semantics></math></inline-formula> containing the monopole) can be considered an excitation of the pressureless and energyless ground state of the confining phase. Correcting an earlier estimate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mn>0</mn></msub></semantics></math></inline-formula>, we show that the vortex-loop self-intersection region associates to the central part of a(n) (anti)caloron and that this region carries one unit of electric U(1) charge via the (electric-magnetic dually interpreted) charge of the monopole. The monopole core quantum vibrates at a thermodynamically determined frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mn>0</mn></msub></semantics></math></inline-formula> and is unresolved. For a deconfining-phase plasma oscillation about the zero-pressure background at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo>=</mo><msub><mi>T</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>, we compute the lowest frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Ω</mo><mn>0</mn></msub></semantics></math></inline-formula> within a neutral and homogeneous spatial ball (no trapped monopole) in dependence of its radius <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula>. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>=</mo><msub><mi>r</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula> a comparison of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Ω</mo><mn>0</mn></msub></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mn>0</mn></msub></semantics></math></inline-formula> reveals that the neutral plasma oscillates much slower than the same plasma driven by the oscillation of a monopole core. |
| first_indexed | 2024-03-09T20:54:42Z |
| format | Article |
| id | doaj.art-a3110a1e39304a5493b10799dbf57afb |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-09T20:54:42Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-a3110a1e39304a5493b10799dbf57afb2023-11-23T22:23:42ZengMDPI AGUniverse2218-19972022-02-018211710.3390/universe8020117On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills ThermodynamicsRalf Hofmann0Thierry Grandou1Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 12, D-69120 Heidelberg, GermanyInstitut de Physique de Nice, Université Cote d’Azur, UMR CNS 7010, 1361 Routes des Lucioles, 06560 Valbonne, FranceFor a pure SU(2) Yang–Mills theory in 4D, we revisit the spatial (3D), ball-like region of radius <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mn>0</mn></msub></semantics></math></inline-formula> in its bulk subject to the pressureless, deconfining phase at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>T</mi><mn>0</mn></msub><mo>=</mo><mn>1.32</mn><mspace width="0.166667em"></mspace><msub><mi>T</mi><mi>c</mi></msub></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula> denotes the critical temperature for the onset of the deconfining–preconfining phase transition. Such a region possesses finite energy density and represents the self-intersection of a figure-eight shaped center-vortex loop if a BPS monopole of core radius ∼<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfrac><msub><mi>r</mi><mn>0</mn></msub><mrow><mn>52.4</mn></mrow></mfrac></semantics></math></inline-formula>, isolated from its antimonopole by repulsion externally invoked through a transient shift of (anti)caloron holonomy (pair creation), is trapped therein. The entire soliton (vortex line plus region of self-intersection of mass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>m</mi><mn>0</mn></msub></semantics></math></inline-formula> containing the monopole) can be considered an excitation of the pressureless and energyless ground state of the confining phase. Correcting an earlier estimate of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>r</mi><mn>0</mn></msub></semantics></math></inline-formula>, we show that the vortex-loop self-intersection region associates to the central part of a(n) (anti)caloron and that this region carries one unit of electric U(1) charge via the (electric-magnetic dually interpreted) charge of the monopole. The monopole core quantum vibrates at a thermodynamically determined frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mn>0</mn></msub></semantics></math></inline-formula> and is unresolved. For a deconfining-phase plasma oscillation about the zero-pressure background at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mo>=</mo><msub><mi>T</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>, we compute the lowest frequency <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Ω</mo><mn>0</mn></msub></semantics></math></inline-formula> within a neutral and homogeneous spatial ball (no trapped monopole) in dependence of its radius <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>R</mi><mn>0</mn></msub></semantics></math></inline-formula>. For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>=</mo><msub><mi>r</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula> a comparison of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Ω</mo><mn>0</mn></msub></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ω</mi><mn>0</mn></msub></semantics></math></inline-formula> reveals that the neutral plasma oscillates much slower than the same plasma driven by the oscillation of a monopole core.https://www.mdpi.com/2218-1997/8/2/117SU(2) Yang-Mills thermodynamicsdeconfining phasecaloronconfining phasecenter-vortex loopelectron |
| spellingShingle | Ralf Hofmann Thierry Grandou On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills Thermodynamics Universe SU(2) Yang-Mills thermodynamics deconfining phase caloron confining phase center-vortex loop electron |
| title | On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills Thermodynamics |
| title_full | On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills Thermodynamics |
| title_fullStr | On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills Thermodynamics |
| title_full_unstemmed | On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills Thermodynamics |
| title_short | On Emergent Particles and Stable Neutral Plasma Balls in SU(2) Yang-Mills Thermodynamics |
| title_sort | on emergent particles and stable neutral plasma balls in su 2 yang mills thermodynamics |
| topic | SU(2) Yang-Mills thermodynamics deconfining phase caloron confining phase center-vortex loop electron |
| url | https://www.mdpi.com/2218-1997/8/2/117 |
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