A Metric-Deformed $q$-Gauge Dirac Equation
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913153831403520 |
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| author | Quiceno, Julio César Jaramillo |
| author_facet | Quiceno, Julio César Jaramillo |
| contents | We construct a family of metric-deformed gauge theories based on a recently introduced $q$-Dirac operator $D_q = γ^μ\sqrt{|g^{μμ}|}\partial_μ$, which arises from a deformed D'Alembertian $\Box_q = |g^{00}|\partial_t^2 - \sum_i |g^{ii}|\partial_i^2$. The deformation parameter $q$ is related to the metric components via $q_μ= \sqrt{|g^{μμ}|}$. By promoting $g^{μμ}(x)$ to spacetime-dependent background fields, we define a deformed covariant derivative $D_μ^{(q)} = \partial_μ+ ieA_μ(x)/\sqrt{|g^{μμ}(x)|}$ (no sum over $μ$). The corresponding field strength $F_{μν}^{(q)} = [D_μ^{(q)}, D_ν^{(q)}]$ acquires new terms proportional to $\partial_μ(1/\sqrt{|g^{νν}|})$, which vanish for constant metrics. We write down gauge-invariant actions for deformed Yang-Mills theory and for fermions minimally coupled to $D_μ^{(q)}$. This work provides a mathematical foundation for $q$-deformed gauge theories from a metric perspective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21508 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Metric-Deformed $q$-Gauge Dirac Equation Quiceno, Julio César Jaramillo Mathematical Physics We construct a family of metric-deformed gauge theories based on a recently introduced $q$-Dirac operator $D_q = γ^μ\sqrt{|g^{μμ}|}\partial_μ$, which arises from a deformed D'Alembertian $\Box_q = |g^{00}|\partial_t^2 - \sum_i |g^{ii}|\partial_i^2$. The deformation parameter $q$ is related to the metric components via $q_μ= \sqrt{|g^{μμ}|}$. By promoting $g^{μμ}(x)$ to spacetime-dependent background fields, we define a deformed covariant derivative $D_μ^{(q)} = \partial_μ+ ieA_μ(x)/\sqrt{|g^{μμ}(x)|}$ (no sum over $μ$). The corresponding field strength $F_{μν}^{(q)} = [D_μ^{(q)}, D_ν^{(q)}]$ acquires new terms proportional to $\partial_μ(1/\sqrt{|g^{νν}|})$, which vanish for constant metrics. We write down gauge-invariant actions for deformed Yang-Mills theory and for fermions minimally coupled to $D_μ^{(q)}$. This work provides a mathematical foundation for $q$-deformed gauge theories from a metric perspective. |
| title | A Metric-Deformed $q$-Gauge Dirac Equation |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2605.21508 |