<< /S /GoTo /D (subsection.3.4) >> (Rayleigh Scattering) 0000032506 00000 n 0000002561 00000 n Quantum theory for light 44 0 obj << /S /GoTo /D (subsubsection.3.4.3) >> Bose-Einstein and Fermi-Dirac distributions 19. 0000026130 00000 n 0000002745 00000 n 0000001583 00000 n 0000024010 00000 n Now that we have gone through quantization of a classical field (Schr¨odinger field so far), we can proceed to quantize the Maxwell field. 1 Canonical Quantization of the Electromagnetic Field Peskin-Schroeder state the Feynman Rules for the photon eld in 4.8: and 0000030035 00000 n 0000013383 00000 n 57 0 obj 0000026006 00000 n 49 0 obj Denteneer Fall 2008. endobj << /S /GoTo /D (subsubsection.3.4.2) >> Introduction and history 3 x2. endobj Identical spin-1 2 particles 17 x8. 0000034827 00000 n 0000039588 00000 n (Vector Potential) 17 0 obj endobj (Hamiltonian) 33 0 obj endobj
Version of 24.10.2018, Page 1 Chapter 2: Quantization of the Electromagnetic Field In this chapter we will develop the fundamentals of quantum-electrodynamics (QET), i.e. 2 SECOND QUANTIZATION x1. << /S /GoTo /D (section.1) >> 73 0 obj 0000032528 00000 n
invariance. and postpone the proof to Chapter 9 Functional Methods. 0000014200 00000 n The N-boson system 4 x3. endobj 0000025255 00000 n 81 0 obj Electromagnetic Field Quantization The canonical momentum is given as ˇ = @L @A_ = F 0 ; Apparently, ˇ 0 = 0, and thus one can not quantize the A0. /Filter /FlateDecode Wei Wang Lectures on QFT October 30, 2017 9 / 19.
It’s an interesting subject, and the basis for consideration of interactions of particles with EM fields (light). 0000011180 00000 n H���yPTG���0�dƇ���7���&��5�/]Q@�AD�>����9�K�S�a0��"�ƒ�qESJŸ&�XZ��. endobj endobj Normal Modes in the Coulomb Gauge In order to quantize the field by the procedure we developed in lecture notes on "quantum field theory", we must introduce a normal mode expansion for the field. 0000033135 00000 n
View Notes - lecture 10 notes from PHY 510 at SUNY Buffalo State College. endobj 0000015414 00000 n (Classical Electromagnetic Field) (Parity) /Length 3189 )G� �������������ş�2;�h-fW73�T̴�Z5�Z�4�������BP>�k��,ؼ��e��۶)w��\��)1C8SH�0�p�gg����~� R�K���}��mU�W�y/�J$��V�%������3U��U�$�j��^6��+��߭����,0�i�!I �fVG��!1����=� �Z�/����(��Mh"#�4|�KA�4Ԍ�ҕ���4�Q�o��K�fU~��f^�����M��Ϥ�%��(3�%��Sy��G������bY����KxѠ��q�X���ElY�˦�%�\�DJ�Wp��Ź�g��k���������.R�^���,$�;���nv:8��!��Ư��+C������zM����w懜�t(d�ch.��r� ���b�����`�0M�CPI��K�'��6�e�F��E�� �E���_`�n�^l¨PD�˲�S6���TfaHD&MC�]2��a��:�G�P�Nͯ�������jU.bk~�i�9��=jcD0�v���/q�*��g��[>4��s�� �\xq��5_�A"��]��e"��R���H;��oq��m|�6�Ĕ����b���Z+1q�@2���֙�.
>> 0000031850 00000 n &F��Z 5 0 obj 0000031604 00000 n << /S /GoTo /D (subsection.1.1) >> 0000024750 00000 n endobj Energy of the field. endobj 77 0 obj (Spinless Schr\366dinger Field) 0000024326 00000 n << /S /GoTo /D [82 0 R /Fit ] >> SECOND QUANTIZATION Lecture notes with course Quantum Theory Dr. P.J.H. 0000014693 00000 n x��ZYo�~ׯ`�(��������6��8�c!�]9��K���в�a��S��\�! << /S /GoTo /D (section.4) >> endobj << /S /GoTo /D (subsection.3.2) >> to, e.g., L. H. Ryder, Quantum Field Theory (Cambridge University Press, 1996)”. (Classical Maxwell Field) The N-fermion system 13 x6. 8.323 LECTURE NOTES 1, SPRING 2008: Quantization of the Free Scalar Field p. 2 For most of this course we will use units for which ¯h ≡ 1, but for now I will leave the ¯h’s in the equations.The HamiltonianH(p i,q i) is then also an operator on the Hilbert space, and in the Schr¨odinger picture the physical states evolve according to the Schr¨odinger 0. 36 0 obj 0000003801 00000 n 9 0 obj Photon creation, annihilation, and number operators. << /S /GoTo /D (subsubsection.3.4.4) >> endobj endobj endobj 64 0 obj endobj
endobj 84 0 obj << must be modified to remove one of these 3 conjugate pairs. 0000019865 00000 n (Quantization of Radiation Field) 76 0 obj 0000014221 00000 n 72 0 obj 1. 0000016789 00000 n endobj
The many-boson system 5 x4. trailer << /Size 114 /Info 54 0 R /Root 56 0 R /Prev 91411 /ID[<8db2c3353b5f51807ff54716fb683d71><8db2c3353b5f51807ff54716fb683d71>] >> startxref 0 %%EOF 56 0 obj << /Type /Catalog /Pages 53 0 R >> endobj 112 0 obj << /S 673 /Filter /FlateDecode /Length 113 0 R >> stream 0000026057 00000 n endobj 29 0 obj �J���d>�z\�y�Y8¨Q�g��f�܄S\�[g���P�������!���ņ=\5�0 �,�R endstream endobj 113 0 obj 658 endobj 57 0 obj << /Type /Page /Parent 53 0 R /Resources 58 0 R /Contents [ 67 0 R 69 0 R 82 0 R 90 0 R 102 0 R 104 0 R 106 0 R 108 0 R ] /MediaBox [ 0 0 612 792 ] /CropBox [ 0 0 612 792 ] /Rotate 0 >> endobj 58 0 obj << /ProcSet [ /PDF /Text ] /Font << /F5 91 0 R /F6 98 0 R /F7 70 0 R /F8 76 0 R /F9 80 0 R /F10 63 0 R /F11 60 0 R /T3 86 0 R >> /ExtGState << /GS1 109 0 R >> >> endobj 59 0 obj << /Type /FontDescriptor /Ascent 698 /CapHeight 681 /Descent -207 /Flags 6 /FontBBox [ -251 -250 1009 969 ] /FontName /JNFFEF+CMR10 /ItalicAngle 0 /StemV 69 /XHeight 434 /CharSet (/quotedblright/H/Y/fi/f/I/dotaccent/v/period/colon/h/P/nine/Delta/F/w/di\ eresis/bracketleft/d/i/L/N/y/zero/j/M/z/n/one/A/k/O/equal/bracketright/t\ wo/m/quoteright/x/three/o/parenleft/ffi/p/E/S/quotedblleft/parenright/fo\ ur/T/q/five/U/g/asterisk/B/r/six/b/tilde/C/plus/s/a/seven/c/W/D/l/comma/\ t/eight/macron/e/exclam/G/hyphen/u) /FontFile3 61 0 R >> endobj 60 0 obj << /Type /Font /Subtype /Type1 /FirstChar 1 /LastChar 77 /Widths [ 917 750 556 722 750 750 681 722 361 750 778 653 625 785 750 681 556 528 394 278 444 764 444 556 500 392 389 833 556 500 306 278 278 556 556 500 500 278 500 500 500 722 528 556 556 500 778 389 389 278 500 528 444 500 528 278 500 500 500 278 278 500 278 500 500 500 333 528 1028 833 833 500 778 278 500 708 306 ] /Encoding 64 0 R /BaseFont /JNFFEF+CMR10 /FontDescriptor 59 0 R /ToUnicode 65 0 R >> endobj 61 0 obj << /Filter /FlateDecode /Length 7287 /Subtype /Type1C >> stream 0000016206 00000 n 32 0 obj �O)��, ���m��Jc��Ӭx^�>���"aY�\������)���0�P�J�E:5����lv'X�[�}>%�����"� �\=�g+Q{%���`A�s�f? Canonical quantization will be. Maxwell’s equations.
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Lecture in Quantum Communication, WS 2018/2019, Friedrich-Schiller-University, Jena Fabian Steinlechner and Falk Eilenberger All notes subject to change, no guarantee to correctness, corrections welcome. << /S /GoTo /D (subsection.3.3) >> 0000033781 00000 n Passing to operators. (Multipole Transitions) 28 0 obj (Interaction With Matter) (Resonant Scattering) 0000026831 00000 n endobj 20 0 obj 0000026151 00000 n B =0: Maxwell-Faraday equation; r⇥E = _ 1 c @B @t (Faraday’s law of induction) Ampere’s circuital law; r⇥B = µ. (Second-order Fermi's Golden Rule) endobj 45 0 obj 16 0 obj Problems with semiclassical description. (Cross Section) 0000016606 00000 n 1 Electromagnetic Fields and Quantum Mechanics Here electromagnetic fields are considered to be quantum objects. (Free Hamiltonian) 1 Electromagnetic Fields and Quantum Mechanics Here electromagnetic fields are considered to be quantum objects. endobj (Casimir Effect) %PDF-1.2 %���� This preview shows page 1 - 5 out of 11 pages. 0000003307 00000 n
endobj It is not possible to maintain explicit Lorentz covariance! }�?G�P˱�Ak����e��k����5O��z����6=mogSPPbn���23�����CO�������98,�asY��ry�O����E,|�,�D�(MUZ��>]�a�����s�\%��6w��@Uccc�h@7� ))���e K�%��хa�Š: j��6v@8�p ��RP�IH�� � ��Ўl dM䁴9�EDxY?h����*�p�X�ö�Mx/�t�K)h���(���r�����L��"�`��ʁI�Nb 52 0 obj To solve problem (2), the standard Hamiltonian quantization procedure of imposing canonical equal time, commutation relations between canonically conjugate coordinates and momenta. 0000034906 00000 n endobj Electromagnetic Field Quantization The canonical momentum is given as ˇ = @L @A_ = F 0 ; Apparently, ˇ 0 = 0, and thus one can not quantize the A0. 0000030350 00000 n 37 0 obj J + µ. We have tutors online 24/7 who can help you get unstuck.
48 0 obj (Dipole Transition Rates) 13 0 obj 0000015743 00000 n 80 0 obj 25 0 obj 0000027525 00000 n outlined below, and path integral quantization in Topic 4. fields of classical electrodynamics are not easy to quantize directly because: (1) If the, are taken as canonical coordinates, then the components of, (2) A free electromagnetic wave has only two independent transverse field components, and quantizing all, three would give three different quanta, whereas real photons have only two spin states, To solve problem (1) and preserve explicit Lorentz invariance, use, and derive the canonically conjugate momenta, which shows that there is no time-like canonical momentum, and the electric field is the canonical momentum, conjugate to the vector potential! Stuck? The many-fermion system 14 x7. 0000012641 00000 n 0000002328 00000 n
40 0 obj 0000019334 00000 n Identical spin-0 particles 8 x5. endobj Quantum theory for light and there is a time-independent constraint on the 3 spatial components. 41 0 obj
<< /S /GoTo /D (subsection.4.1) >> 0000027054 00000 n 0000025303 00000 n
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