CAJ | 학술논문

重新考虑了D＋1维闵可夫斯基时空中p维超立方体腔里的标量场的热卡西米尔效应。经过标准的量子场论方法处理后，热卡西米尔自由能可以分为零温部分和有限的与温度有关的部分。在此前的一些文献中，由于含温度的部分自身是有限的，这部分的正则化被忽视了，而无穷远处卡西米尔能量的收敛性以及卡西米尔力的消失又要求对这部分进行正则化。利用Zeta函数方法和Abel-Plana公式，严格推导了自由能零温部分和含温部分的正则化。在D＝3，p＝1和D＝p＝3的情况下准确地恢复了文献中平行板和三维盒子的结果。并且给出了卡西米尔自由能高温（大间隔）和低温（小间隔）展开的精确表达式，并由此验证了在零温和含温两部分自由能都正则化后，对于不同的边界条件，在无穷远处卡西米尔力总是趋于零。
중신고필료D＋1유민가부사기시공중p유초립방체강리적표량장적열잡서미이효응。경과표준적양자장론방법처리후，열잡서미이자유능가이분위령온부분화유한적여온도유관적부분。재차전적일사문헌중，유우함온도적부분자신시유한적，저부분적정칙화피홀시료，이무궁원처잡서미이능량적수렴성이급잡서미이력적소실우요구대저부분진행정칙화。이용Zeta함수방법화Abel-Plana공식，엄격추도료자유능령온부분화함온부분적정칙화。재D＝3，p＝1화D＝p＝3적정황하준학지회복료문헌중평행판화삼유합자적결과。병차급출료잡서미이자유능고온（대간격）화저온（소간격）전개적정학표체식，병유차험증료재령온화함온량부분자유능도정칙화후，대우불동적변계조건，재무궁원처잡서미이력총시추우령。
We reconsider the thermal scalar Casimir effect for p-dimensional hypercubic cavity inside D+1-dimensional Minkowski space-time.The thermal Casimir free energy can be divided into the divergent zero-temperature part and the automatically finite temperature-dependent part through standard quantum field theory treatments.Due to the finiteness,the regularization of the temperature-dependent part,which is also required for the convergency of the Casimir energy and the vanishing of the Casimir force with the separation increasing to infinity,is neglected in some literatures.We derive rigorously the regularization of the zero temperature part as well as the temperature-dependent part of the free energy by making use of the zeta function technique and the Abel-Plana formula.In the ca-ses of D=3 ,p=1 and D=3 ,p=3 ,we precisely recover the results of parallel plates and three-di-mensional box in the literature.And explicit expressions of the Casimir free energy in both low tem-perature (small separations)and high temperature (large separations)regimes are given,through which we find that after the regularization of both parts,with the side length going to infinity the force always tends to zero for different boundary conditions.Our study may be helpful in providing a com-prehensive and complete understanding of this old problem.