本論文旨在探討量子電動力學的真空在電磁場作用下的新現象。本文共有兩部份︰第一部份探討在邊界效應和電磁場共同引起的電流，而第二部份則探討在電磁場導致的自旋流。

在第一部份，我們將重新研究關於「施加電磁場，量子效應會在邊界附近產生電流」的問題。我們把結果推廣至非共形場論，以包含電子質量帶來的修正。我們的結果也可以推廣到兩個平行邊界所引起的電流。

在第二部份，我們將證明電磁場在真空可引起自旋流。此外，我們亦提出了一個實驗，透過測量向列相液晶的扭轉角度，來觀測自旋流伴隨的自旋力矩。

In this thesis, we are going to study the novel phenomena of the QED vacuum under a background electromagnetic field. It consists of two parts: the first part focus on the electric current induced by the boundary effect together with the background electromagnetic field; while the second part focus on the spin current induced by the background electromagnetic field.

In the first part, we re-examined the problem about the quantum generation of electric current near the vicinity of the boundary when an electromagnetic field is applied \cite{CsChu}. We used another method to extend the result to non-conformal field theory, by including the correction of finite electron mass. Moreover, we used this method to study the more general problem of the quantum generation of electric current between two parallel boundaries.

In the second part, we showed that the vacuum under a background electromagnetic field would induce a spin current. We also proposed an experiment to observe the spin torque exerted by the spin current by measuring the twisted angle of the director axis of a nematic liquid crystal.

Bibliography
[1] C.-S. Chu and R.-X. Miao, “Weyl anomaly induced current in boundary quantum field theories,” Phys. Rev. Lett., vol. 121, p. 251602, Dec 2018.
[2] K. Fujikawa and H. Suzuki, Path integrals and Quantum Anomalies. Clarendon, 2004.
[3] V. Alonso, S. D. Vincenzo, and L. Mondino, “On the boundary conditions for the dirac equation,” European Journal of Physics, vol. 18, pp. 315–320, sep 1997.
[4] G. Esposito and K. Kirsten, “Chiral bag boundary conditions on the ball,”Phys. Rev. D, vol. 66, p. 085014, Oct 2002.
[5] F. Gross, Relativistic Quantum Mechanics and field theory. Wiley-VCH Verlag, 2006.
[6] M. E. Peskin and D. V. Schroeder, An introduction to quantum field theory. Perseus Books, 1995.
[7] B. Johnson, “Generalized lerch zeta function,” Pacific Journal of Mathematics, vol. 53, no. 1, p. 189–193, 1974.
[8] H. Bateman and A. Erd ́elyi, Higher transcendental functions. McGraw-Hill Book Co, 1953.
[9] P.-J. Hu, Q.-L. Hu, and R.-X. Miao, “Note on anomalous currents for a free theory,” Phys. Rev. D, vol. 101, p. 125010, Jun 2020.
[10] E. I. Rashba, “Spin currents in thermodynamic equilibrium: The challenge of discerning transport currents,” Phys. Rev. B, vol. 68, p. 241315, Dec 2003.
[11] A. Vernes, B. L. Gy ̈orffy, and P. Weinberger, “Spin currents, spin-transfer torque, and spin-hall effects in relativistic quantum mechanics,” Phys. Rev. B, vol. 76, p. 012408, Jul 2007.
[12] H. Bauke, S. Ahrens, C. H. Keitel, and R. Grobe, “What is the relativistic spin operator?,” New Journal of Physics, vol. 16, p. 043012, apr 2014.
[13] V. Bargmann and E. P. Wigner, “Group theoretical discussion of relativistic wave equations,” Proceedings of the National Academy of Sciences, vol. 34, no. 5, pp. 211–223, 1948.
[14] D. M. Fradkin and R. H. Good, “Electron polarization operators,” Rev. Mod. Phys., vol. 33, pp. 343–352, Apr 1961.
[15] X.-G. Huang, M. Matsuo, and H. Taya, “Spontaneous generation of spin current from the vacuum by strong electric fields,” Progress of Theoretical and Experimental Physics, vol. 2019, 11 2019. 113B02.
[16] J. C. Collins, Renormalization an introduction to renormalization,the renormalization group and the operator-product expansion. Cambridge University Press, 1984.
[17] F. Schwabl, Advanced Quantum Mechanics. Springer, 2008.
[18] J. D. Bjorken and S. D. Drell, Relativistic Quantum Mechanics. McGraw-Hill, 1964.
[19] J. Smit, “The spontaneous hall effect in ferromagnetics i,” Physica, vol. 21, no. 6, pp. 877–887, 1955.
[20] J. Smit, “The spontaneous hall effect in ferromagnetics ii,” Physica, vol. 24, no. 1, pp. 39–51, 1958.
[21] L. Berger, “Side-jump mechanism for the hall effect of ferromagnets,” Phys. Rev. B, vol. 2, pp. 4559–4566, Dec 1970.
[22] L. Berger, “Application of the side-jump model to the hall effect and nernst effect in ferromagnets,” Phys. Rev. B, vol. 5, pp. 1862–1870, Mar 1972.
[23] L. D. Landau, L. P. Pitaevskii, and E. M. Lifshitz, Electrodynamics of Continuous Media. Butterworth-Heinemann, 1984.
[24] D. A. T. Somers and J. N. Munday, “Rotation of a liquid crystal by the casimir torque,” Phys. Rev. A, vol. 91, p. 032520, Mar 2015.
[25] D. A. T. Somers, J. L. Garrett, K. J. Palm, and J. N. Munday, “Measurement of the casimir torque,” Nature, vol. 564, pp. 386–389, Dec 2018.
[26] I.-C. Khoo, Liquid crystals. J. Wiley, 2007.
[27] A. Stoddart and R. Viollier, “Evaluating loop diagrams in a cavity (ii). the vacuum polarization in scalar qed,” Nuclear Physics A, vol. 541, no. 4, pp. 623–640, 1992.
[28] W. Greiner and J. Reinhardt, Quantum electrodynamics. - 4th ed. Springer, 2009.