Wick Theorem and Hopf Algebra Structure in Causal Perturbative Quantum Field Theory
We consider the general framework of perturbative quantum field theory for the pure Yang–Mills model. We give a more precise version of the Wick theorem using Hopf algebra notations for chronological products and not for Feynman graphs. Next, we prove that the Wick expansion property can be preserve...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-02-01
|
| Series: | Universe |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-1997/9/3/117 |
| _version_ | 1797608753527259136 |
|---|---|
| author | D. R. Grigore |
| author_facet | D. R. Grigore |
| author_sort | D. R. Grigore |
| collection | DOAJ |
| description | We consider the general framework of perturbative quantum field theory for the pure Yang–Mills model. We give a more precise version of the Wick theorem using Hopf algebra notations for chronological products and not for Feynman graphs. Next, we prove that the Wick expansion property can be preserved for all cases in order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula>. However, gauge invariance is broken for chronological products of Wick submonomials. |
| first_indexed | 2024-03-11T05:47:55Z |
| format | Article |
| id | doaj.art-386f4eaee93e43e09695fdbc0b64d346 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-03-11T05:47:55Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-386f4eaee93e43e09695fdbc0b64d3462023-11-17T14:15:41ZengMDPI AGUniverse2218-19972023-02-019311710.3390/universe9030117Wick Theorem and Hopf Algebra Structure in Causal Perturbative Quantum Field TheoryD. R. Grigore0Department of Theoretical Physics, Institute for Physics and Nuclear Engineering “Horia Hulubei”, 077125 Măgurele, RomaniaWe consider the general framework of perturbative quantum field theory for the pure Yang–Mills model. We give a more precise version of the Wick theorem using Hopf algebra notations for chronological products and not for Feynman graphs. Next, we prove that the Wick expansion property can be preserved for all cases in order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></semantics></math></inline-formula>. However, gauge invariance is broken for chronological products of Wick submonomials.https://www.mdpi.com/2218-1997/9/3/117perturbative quantum field theorycausal approachpure Yang-Mills fields |
| spellingShingle | D. R. Grigore Wick Theorem and Hopf Algebra Structure in Causal Perturbative Quantum Field Theory Universe perturbative quantum field theory causal approach pure Yang-Mills fields |
| title | Wick Theorem and Hopf Algebra Structure in Causal Perturbative Quantum Field Theory |
| title_full | Wick Theorem and Hopf Algebra Structure in Causal Perturbative Quantum Field Theory |
| title_fullStr | Wick Theorem and Hopf Algebra Structure in Causal Perturbative Quantum Field Theory |
| title_full_unstemmed | Wick Theorem and Hopf Algebra Structure in Causal Perturbative Quantum Field Theory |
| title_short | Wick Theorem and Hopf Algebra Structure in Causal Perturbative Quantum Field Theory |
| title_sort | wick theorem and hopf algebra structure in causal perturbative quantum field theory |
| topic | perturbative quantum field theory causal approach pure Yang-Mills fields |
| url | https://www.mdpi.com/2218-1997/9/3/117 |
| work_keys_str_mv | AT drgrigore wicktheoremandhopfalgebrastructureincausalperturbativequantumfieldtheory |