O（$N$）普适类的鲁棒性
Robustness of the O($N$) universality class
摘要：
用两种独立的方法计算了洛伦兹破坏O（$N$）$λϕ^{4}$标量场理论的临界指数.在第一种情况下，我们重新正规化一个无质量的理论，利用正规化条件。在第二种情况下，在同一理论的大规模版本中完成了相同的任务，先前在四维中的BPHZ方法中重整化。结果表明，尽管重整化常数、$β$和反常维数都得到了Lorentz破坏的量子修正，但两种方法得到的临界指数是相同的，而且与Lorentz不变的结果是相等的.最后，我们概括了所有循环水平的最后两个结果，我们提供了对称性参数来证明后者。
英文摘要：
We calculate the critical exponents for Lorentz-violating O($N$) $λϕ^{4}$ scalar field theories by using two independent methods. In the first situation we renormalize a massless theory by utilizing normalization conditions. An identical task is fulfilled in the second case in a massive version of the same theory, previously renormalized in the BPHZ method in four dimensions. We show that although the renormalization constants, the $β$ and anomalous dimensions acquire Lorentz-violating quantum corrections, the outcome for the critical exponents in both methods are identical and furthermore they are equal to their Lorentz-invariant counterparts. Finally we generalize the last two results for all loop levels and we provide symmetry arguments for justifying the latter.
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