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arXiv 1804.06503hep-thcond-mat.stat-mechmath-phmath.MP
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标量场理论中全圈紫外辐射的严格Lorentz破坏发散

Exact Lorentz-violating all-loop ultraviolet divergences in scalar field theories

P. R. S. Carvalho, M. I. Sena-Junior

摘要:

在这项工作中,我们分析评估的紫外线发散的洛伦兹破坏的大质量O($N$)$λϕ^{4}$标量场理论,这是准确的洛伦兹破坏机制,首先明确在次领先的顺序,后者在任何循环水平通过归纳过程的基础上的定理从精确的方法,计算相应的临界指数。为了达到这个目的,我们采用了三种不同的和独立的场论重整化群方法。结果表明,临界指数在三种不同的方法是相同的,等于他们的洛伦兹不变的同行。此外,我们表明,在这里得到的结果,基于相应的$β$ -功能和异常尺寸的引用项的循环顺序的单一概念,减少到通过早期的非精确方法的基础上联合重新定义的字段和耦合常数的理论,在适当的限制。

英文摘要:

In this work we evaluate analytically the ultraviolet divergences of Lorentz-violating massive O($N$) $λϕ^{4}$ scalar field theories, which are exact in the Lorentz-violating mechanism, firstly explicitly at next-to-leading order and latter at any loop level through an induction procedure based on a theorem following from the exact approach, for computing the corresponding critical exponents. For attaining that goal, we employ three different and independent field-theoretic renormalization group methods. The results found for the critical exponents show that they are identical in the three distinct methods and equal to their Lorentz invariant counterparts. Furthermore, we show that the results obtained here, based on the single concept of loop order of the referred terms of the corresponding $β$-function and anomalous dimensions, reduce to the ones obtained through the earlier non-exact approach based on a joint redefinition of the field and coupling constant of the theory, in the appropriate limit.

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