1794-AENTRXT 在上一個(gè)系列“超越局域近似-費(fèi)曼圖展開（1）”中，我們看到了高階頂角函數(shù)對(duì)于自能修正的神奇之處。通過將不同格點(diǎn)上的局域兩粒子頂角函數(shù)用非局域項(xiàng)連接起來，我們可以得到對(duì)于動(dòng)力學(xué)平均場(chǎng)局域自能的非局域修正。這讓我們對(duì)于頂角函數(shù)的作用有了新的認(rèn)識(shí)和理解。頂角函數(shù)不再只是作為Bethe-Salpeter方程中的一部分，總是與各種極化率綁定在一起。高階頂角函數(shù)與低階頂角函數(shù)之間的關(guān)系，讓我們多了一種構(gòu)造量子多體理論的途徑。今天，我們來進(jìn)一步聊聊兩粒子頂角函數(shù)的有趣之處。
我們首先來介紹一下兩粒子格林函數(shù)。和單粒子格林函數(shù)類似，它代表的是多粒子體系對(duì)于增加和減少兩個(gè)粒子的響應(yīng)，可以依照單粒子格林函數(shù)的樣子類似定義
這里我們用1,2,3,4表示一系列聯(lián)合指標(biāo)，可以包括動(dòng)量、自旋等。如果作用量S是無相互作用的，我們可以對(duì)四費(fèi)米算符應(yīng)用Wick分解，分別得到兩個(gè)單粒子傳播子的乘積，
然而，如果S含有相互作用項(xiàng)時(shí)，就會(huì)多出一項(xiàng)，對(duì)應(yīng)的是4費(fèi)米子不可分的收縮項(xiàng)。
我們對(duì)單粒子格林函數(shù)很熟悉，知道它有兩個(gè)外腳，其他部分對(duì)應(yīng)自能的貢獻(xiàn)。
相應(yīng)的，我們可以理解，兩粒子格林函數(shù)應(yīng)該有四個(gè)外腳，同時(shí)還有類似于自能一樣的東西，如下圖所示。
這三項(xiàng)，分別對(duì)應(yīng)了上述公式中兩粒子格林函數(shù)的三個(gè)貢獻(xiàn)。其中，陰影部分的圖形是兩粒子格林函數(shù)的“自能”部分，我們通常稱之為完全頂角函數(shù)(fullvertexfunction)。這里我們沒有畫成類似于單粒子格林函數(shù)Dyson方程那樣的迭代方式，而是把它收縮成一個(gè)整體。這是因?yàn)閮闪Ｗ訉哟紊系摹癉yson方程”形式上變得比較復(fù)雜了，還需要慢慢聊。大部分人可能都是通過如下的兩個(gè)途徑了解到兩粒子頂角函數(shù)：
1.單粒子格林函數(shù)求導(dǎo)；
2.Bethe-Salpeter方程。其實(shí)兩者是一回事。前面我們提到過，通常我們推導(dǎo)關(guān)聯(lián)函數(shù)是在作用量中添加一個(gè)高斯形式的源項(xiàng)，然后對(duì)源項(xiàng)求導(dǎo)。這里我們要計(jì)算的是具有四費(fèi)米子算符的兩粒子格林函數(shù)，所以我們需要對(duì)單粒子格林函數(shù)求源項(xiàng)的導(dǎo)數(shù)，才能構(gòu)造出四費(fèi)米子算符的乘積。這里，我們要稍微注意一下源項(xiàng)是如何進(jìn)入到格林函數(shù)中的。源項(xiàng)的算符具有高斯型，因此會(huì)在無相互作用格林函數(shù)里出現(xiàn)，通過Dyson方程，也會(huì)出現(xiàn)在自能中。所以，單粒子格林函數(shù)對(duì)源項(xiàng)的求導(dǎo)，包含了對(duì)單粒子無相互作用格林函數(shù)部分的求導(dǎo)，也包含了對(duì)自能的求導(dǎo)。前者會(huì)給出上述圖形中前兩項(xiàng)，而自能對(duì)于源項(xiàng)的求導(dǎo)給出的就是頂角函數(shù)及其連續(xù)遞推公式Bethe-Salpeter方程。因?yàn)槭墙炭茣系闹R(shí)，這里我們不再做更詳細(xì)的介紹了。取決于自能中對(duì)單粒子格林函數(shù)的出現(xiàn)方式不同，我們會(huì)得到三個(gè)不同的Bethe-Salpeter方程，如下圖所示。這是我們通常所說的particle-holehorizontalchannel、particle-holeverticalchannel及particle-particlechannel中的Bethe-Salpeter方程。這是我們這篇所討論內(nèi)容的出發(fā)點(diǎn)。
1794-AENTRXT
NATIONAL INSTRUMENT FP-TB-01 USPP FPTB01
NATIONAL INSTRUMENT FP-TB-1 USPP FPTB11
NATIONAL INSTRUMENT FUS-130 NSPP FUS130
National Instruments NI SCXI-1162HV 32 Channel Module
National Instruments Daq Card 700 Data Aquisition
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NATIONAL INSTRUMENTS GPIB-120A BUS EXPANDER / ISOLATOR
NATIONAL INSTRUMENTS SCXI-1160 16 CHANNEL SPDT RELAY
National Instruments MKI-2/M2 777164-02 Cable; 2 Meter
1784
MFR. PART NUMBER DESCRIPTION
ALLEN BRADLEY 1784-CP CABLE ASSY, 10.5'/3.2M, PEER TO PEER, 9-PIN D SHELL
ALLEN BRADLEY 1784-CP2 CABLE ASSY, 10.5'/3.2M, PEER TO PEER,15-PIN D SHELL,
ALLEN BRADLEY 1784-CAS CABLE 9.5 FT/2.90 M
ALLEN BRADLEY 1784-CP10 CABLE ASSEMBLY 10FT/3.20M IBM AT OR COMPATIBLE
ALLEN BRADLEY 1784-CP14 1784-KTX -KTXD (6-PIN PHOENIX TO RJ-45)
ALLEN BRADLEY 1784-CP15 1784-KTX (CUSTOM ORB TO 15-PIN D-SHELL)
ALLEN BRADLEY 1784-CP16 1784-KTX (CUSTOM ORB TO 25-PIN D-SHELL)
ALLEN BRADLEY 1784-CP2 CABLE ASSY 10 FT/3.20 M 1784-KTP -KT -KT2 KL
ALLEN BRADLEY 1784-CP3 CABLE ASSY 10 FT/3.20 M 1784-KTP -KT -KT2 KL
ALLEN BRADLEY 1784-CP5 CABLE ASSY 10FT/3.20M 1784-KTK1
ALLEN BRADLEY 1784-CP6 CABLE ASSEMBLY 10FT/3.05M KT/KT2/KL TO PLC-5 DIN
ALLEN BRADLEY 1784-CP7 ADAPTER CP/CP5 TO PLC-5 (DIN)
ALLEN BRADLEY 1784-CP8 FOR 1784-KT -KT2 -KL
ALLEN BRADLEY 1784-KR PC/DH-485 INTERFACE MODULE
ALLEN BRADLEY 1784-KT PROCESSOR COMMUNICATION INTERFACE MODULE,
ALLEN BRADLEY 1784-KT2 INTERFACE BOARD
ALLEN BRADLEY 1784-KTC CONTROLNET (1.25 ONLY) ISA/EISA BUS INTERFACE
ALLEN BRADLEY 1784-KTX COMM INTF BOARD
ALLEN BRADLEY 1784-KTXD COMM INTF BOARD
ALLEN BRADLEY 1784-PCC CONTROLNET PCMCIA COMMUNICATION CARD
ALLEN BRADLEY 1784-PCD COMM CARD
ALLEN BRADLEY 1784-PCD1 PC CARD CONNECTOR 5-POSITION OPEN-STYLE HEADER
ALLEN BRADLEY 1784-PCID PCI BUS EXPLICIT MESSAGING CARD
ALLEN BRADLEY 1784-PCIDS PCI BUS TO DEVICENET INTERFACE W/SCANNER FUNCTION
ALLEN BRADLEY 1784-PCIDSLINX DNET SCANNER
ALLEN BRADLEY 1784-PCM4 CABLE 10 FT/ 3.2 M
ALLEN BRADLEY 1784-PCM5 PLC-5/PCMCIA COMMUNICATIONS CABLE
ALLEN BRADLEY 1784-PMC6 1784-PCMK DH+ COMMUNICATION CABLE 8 PIN DIN
ALLEN BRADLEY 1784-PCMC PCMCIA 1784-PCMK COMMUNICATION CARD
ALLEN BRADLEY 1784-PCMK PCMCIA COMMUNICATIONS CARD
ALLEN BRADLEY 1784-PKTX PCI BUS CARD W/ DH+ DH485 RIO SCANNER
1784-U2CN
1784-U2DHP
1784-U2DN
1784-PCMKS
1784-PKTX
1784-PKTXD
1784-PCIC
1784-PCICS
1784-PCIDS
1784-CPCIDS
1784-KTCX
1784-KTCX15
1785
MFR. PART NUMBER DESCRIPTION
ALLEN BRADLEY 1785-ACC5LA ACCESSORY KIT FOR PLC-5/11,5/20
ALLEN BRADLEY 1785-ACC5LB ACCESSORY KIT FOR PLC-5/30 OR HIGHER
ALLEN BRADLEY 1785-ACC5LT ACCESSORY KIT FOR CLASSIC PLC-5
ALLEN BRADLEY 1785-BCM PLC-5 BACKUP COMM MOD
ALLEN BRADLEY 1785-BEM PLC-5 BACKUP COMMUNICATIONS EXPANSION MODULE
ALLEN BRADLEY 1785-CHORAD REMOTE ACCESS MODEM KIT FOR CONN TO SER.CHAN PLC5
ALLEN BRADLEY 1785-CHORADC3B MODEM CABLE FOR PLC-5 TO MODEM
ALLEN BRADLEY 1785-CHBM BACKUP MEMORY CARTRIDGE
ALLEN BRADLEY 1785-ENET PLC-5 ETHERNET/IP EXPANSION MODULE FOR PLC-5
ALLEN BRADLEY 1785-KA DATA HGWY PLUS INTERFACE MODULE,
ALLEN BRADLEY 1785-KA3 PLC-2 DATA HGWY PLUS COMM ADAPTER MOD
ALLEN BRADLEY 1785-KA5 COMM MODULE DATA HWY PLUS TO DATA HWY 485
ALLEN BRADLEY 1785-KA5P COOMUNICATION MODULE,PANEL MOUNT
ALLEN BRADLEY 1785-KE DATA HGWY PLUS RS232 INTERFACE MOD
ALLEN BRADLEY 1785-L11B PLC-5/11 PROCESSOR, (1) DH+/RIO PORT, 8K MEMORY,
ALLEN BRADLEY 1785-L20B PLC-5/20 PROCESSOR (1) DH+/RIO PORT, (1) DH+ PORT W/16K
MEMORY,
ALLEN BRADLEY 1785-L20C15 PLC-5/20C FOR CONTROLNET PHASE 1.5
ALLEN BRADLEY 1785-L20E PLC 5/20 ETHERNET CONTROLLER 16K WORD SRAM
ALLEN BRADLEY 1785-L26B PROTECTED PLC 5/20 CONTROLLER, 16K WORD SRAM
ALLEN BRADLEY 1785-L30B PLC-5/30 CONTROLLER,32K WORD SRAM
ALLEN BRADLEY 1785-L40B PLC 5/40 PROCESSOR
ALLEN BRADLEY 1785-L40C15 PLC-5/40C FOR CONTROLNET PHASE 1.5
ALLEN BRADLEY 1785-L40E PLC 5/40 ETHERNET CONTROLLER, 48K WORD SRAM
ALLEN BRADLEY 1785-L40L EXTENDED LOCAL 5/40, 48K SRAM
ALLEN BRADLEY 1785-L46B PROCESSOR MODULE PLC5/40 48K WORD SRAM, PROTECTED
ALLEN BRADLEY 1785-L46C15 PROTECTED PLC 5/40 CONTROLLER, 48K WORD SRAM
ALLEN BRADLEY 1785-L60B CONTROLNET PLC-5/60 CTRLR,64K WORD SRAM
ALLEN BRADLEY 1785-L60L LOCAL PROCESSOR 64K SRAM
ALLEN BRADLEY 1785-L80B PLC 5/80 CONTROLLER 100K WORD SRAM
ALLEN BRADLEY 1785-L80C15 PLC 5/80 CONTROLNETPHASE 1.5
ALLEN BRADLEY 1785-L80E ETHERNET/IP PLC-5/80 CONTROLLER 100K WORD SRAM
ALLEN BRADLEY 1785-L86B PLC 5/80 CONTROLLER 100K WORD SRAM
ALLEN BRADLEY 1785-LT PLC-5/15 PROCESSOR MODULE, 6K MEMORY
ALLEN BRADLEY 1785-LT2 PLC-5/25 PROCESSOR MODULE, 13K MEMORY
ALLEN BRADLEY 1785-LT3 PLC-5/12 PROCESSOR MODULE, 6K MEMORY
ALLEN BRADLEY 1785-LT4 PLC-5/10 PROCEESOR MODULE, 6K MEMORY
ALLEN BRADLEY 1785-M100 PLC-5/80 EEPROM MEMORY CARTRIDGE,100K
ALLEN BRADLEY 1785-ME16 EEPROM MEMORY CARTRIDGE
ALLEN BRADLEY 1785-ME32 PLC-5/30 EEPROM MEMORY CARTRIDGE
ALLEN BRADLEY 1785-ME64 PLC-5/40 5/60 EEPROM MEMORY CARTRIDGE
ALLEN BRADLEY 1785-MJ 8K EEPROM MEM
ALLEN BRADLEY 1785-MK 16K EEPROM CARTRIDGE
ALLEN BRADLEY 1785-MS PLC-5 8K RAM MEMORY MODULE
National Instruments FP-DI-330 Universal Input
National Instruments FP-DI-330 8-Channel Input Module
IC693MDL648 IC693MDL653 IC693MDL654
IC693MDL655 IC693MDL660 IC693MDL730
IC693MDL731 IC693MDL732 IC693MDL733
IC693MDL734 IC693MDL740 IC693MDL741
IC693MDL742 IC693MDL748 IC693MDL752
IC693MDL753 IC693MDL754 IC693MDL760
IC693MDL916 IC693MDL930 IC693MDL931
IC693MDL940 IC693MDR390 IC693MLX000
IC693MSC301 IC693NIU004 IC693PBM200
IC693PBS201 IC693PCM300 IC693PCM301
IC693PCM311 IC693PIF301 IC693PIF350
IC693PIF400 IC693PRG300 IC693PTM100
IC693PTM101 IC693PWR321 IC693PWR322
IC693PWR324 IC693PWR328 IC693PWR330
IC693PWR331 IC693PWR332 IC693TCM302
IC693TCM303
IC697ACC621 IC697ACC624
IC697ACC644 IC697ACC700 IC697ACC701
IC697ACC702 IC697ACC715 IC697ACC720
IC697ACC721 IC697ACC722 IC697ACC723
IC697ACC724 IC697ACC726 IC697ACC727
IC697ACC728 IC697ACC729 IC697ACC730
IC697ACC732 IC697ACC735 IC697ACC744
IC697ACC775 IC697ACC800 IC697ACC801
IC697ACC802 IC697ACC803 IC697ACC804
IC697ACC805 IC697ACC820 IC697ACC821
IC697ACC822 IC697ADC701 IC697ADS701
IC697ALG230 IC697ALG234 IC697ALG320
IC697ALG324 IC697ALG440 IC697ALG441
IC697ALG444 IC697ALG445 IC697BEM711
National Instruments GPIB-VXI/C VXI Module 181520G-0110
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NATIONAL INSTRUMENTS MICRO GPIB CABLE
NATIONAL INSTRUMENTS NI PCMCIA-GPIB #186736C-01 Tested
NEW NATIONAL INSTRUMENTS MEMORY 128 MB SDRAM 777885-128
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National Instruments NB-DMA-8 Direct Memory Access GPIB
National Instruments NI-HSDIO Driver version 1.4 New
National Instruments NB-A0-6 Digital - Converter Card
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NATIONAL INSTRUMENT NI-CFP-DI-301 USPP NICFPDI301
NATIONAL INSTRUMENTS PC-DI0-96 PCDI096 DAQ BOARD
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National Instruments/Tektronix GPIB adapter 180212-01 A
NATIONAL INSTRUMENTS AT-GPIB/TNT PLUG N PLAY IEEE488.2
National Instruments PCI-6521 Industrial Relay & IO
National Instruments CB-100 I/O Connector Block Kit
National Instruments BNC-2095 w/SH96-96 1-Meter Cable
National Instruments SC-2062, 8-Channel Relay Kit *NEW*
National Instruments PCMCIA-485/2, 2-Port RS485 Cables
National Instruments PCI-6512 Isolated 64-Ch Outputs
NATIONAL INSTRUMENT FUS-130 USPP FUS130
National Instruments Dual Channel 3-32 VDC FP-DI-DC 2pc
National Instruments 180515-01 National Instruments 180
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NATIONAL INSTRUMENTS, SCXI-1162HV, HIGH VOLT DIG INPUT
NATIONAL INSTRUMENTS AT- GPIB MODEL 181060-01 NEW NOS
NATIONAL INSTRUMENTS SCXI-1163R 32 CHANNEL S/S RELAY
NATIONAL INSTRUMENTS SCXI-1121 MODULE 4 CHANNEL AMP
National Instruments SCXI-1100
National Instruments PCI-6503 185183A-01 *NEW*
NATIONAL INSTRUMENTS FP-TB-1 UNIVERSAL TERMINAL BASE
NATIONAL INSTRUMENT NI-CFP-DO-400 USPP NICFPDO400
NATIONAL INSTRUMENT SCXI-1300 USPP SCXI1300
NATIONAL INSTRUMENT FP-TB-1 NSPP FPTB1
National Instruments Pci Gpib 778032-01
NATIONAL INSTRUMENT 185695A-01 NSFP 185695A01
National Instruments 181-7617-1C SCSI Card - ZX-Box Int
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National Instruments 182826C-01 NI PCMCIA-GPIB+ Card
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National Instruments 186736C-01 PCMCIA-GPIB Card
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National Instruments NI PCI-6024E DAQ BOARD
NATIONAL INSTRUMENT SCXI-1302 USPP SCXI1302
National Instruments 779301-512 MB Upgrade PXI-8196/95
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NEW NATIONAL INSTRUMENTS LABVIEW 6i PRO DEV SOFTWARE
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National Instruments NI Hi Speed PCI-6251 M Series DAQ
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National Instruments AT-MIO-16KE-10 16 bit DAQ
National Instruments NI PXI-8171 Card parts as is
NATIONAL INSTRUMENTS 182885E-01 PLUG/PLAY CARD
National Instruments NI PCI-MIO-16E-1 PCI-6070E card
National Instruments 181340D-31 SCSI Controller
National Instruments NI AT-MIO/AI-16XE-10 Multifunction
NI NATIONAL INSTRUMENTS VXI-MXI-2 183345D-03 VXI
National Instruments GPIB-232CV IEEE488-RS232 Converter
National Instruments GPIB-PRL IEEE488-Parallel Conv.
National Instruments Discrete Output Module FP-DO-400
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National Instruments PC-DIO-24/PNP
National Instruments PCIStep PCI STEP Card184903A-14
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National Instruments NI-VXI Text Utilities Ref. Manual
NATIONAL INSTRUMENTS NI PCI-DIO-96 Digital DAQ Board
NATIONAL INSTRUMENTS NI PCI-DIO-96 Board 182920D-01
NATIONAL INSTRUMENTS NI PC-DIO-24/PNP ISA 183873B-01
NATIONAL INSTRUMENTS NI PCI Serial RS-232-485 2 port
3pcs National Instruments AT-MIO-16D/AT-AO-6/10 DAC PCB
A77921 National Instruments PCI-GPIB Board 183617F-01
NATIONAL INSTRUMENTS NI AT-MIO/AI-16XE-10 MULTIFUNCTION
National Instruments: 181830E-01 AT-GPIB/TNT Card
National Instruments GPIB 422CV 256K 180465-02 Rev B1
National Instruments NB-DIO-24, New In Box.
National Instruments P/N 182801A-002 MXI2-1 2 m Cable
National Instruments: 180950-01, SC-2070 Board, Rev. D
NEW NATIONAL INSTRUMENTS PCI 232/485 8CH W/ CABLE
NATIONAL INSTRUMENTS AT-GPIB/TNT ASSY. 181830E-01 488.2
National Instruments BNC-2095 32 BNC connector
NATIONAL INSTRUMENTS GPIB-120A BUS EXPANDER/ISOLATOR
National Instruments SH48-48-A Shielded Cable 183229-01
NI National Instruments PCMCIA-232/4
National Instruments NI SH100-100-F FLEX 185095-02 2 m
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LOT NATIONAL INSTRUMENTS COMBO SOFTWARE DAQMX PXI SCXI
LOT 2 NATIONAL INSTRUMENTS 185196A CABLE 1M SH6868-8DB9
National Instruments SCX-1000 with 2x 1160 Modules
LOT NATIONAL INSTRUMENTS DAQ DAQMX SOFTWARE COMBO KIT
LOT NATIONAL INSTRUMENTS DAQ DAQMX SOFTWARE KITS NEW
NATIONAL INSTRUMENTS PCI-6516 DIGITAL SOURCE OUTPUT DAQ
NI National Instruments DIO Card ISA PC-DIO-96/PnP
National Instruments AT-MIO-16 Data Acquisition Card NI
National Instruments CB-68LPR , LNC
National Instruments NI 4351 PCI Datalogger Card
National Instruments PCI-7314 Stepper Controller 4-Axis
National Instruments PCI-7314 Stepper Controller 4-Axis
NATIONAL INSTRUMENTS 100 Pin 2m Cbl SH100-100-F SAVE$79
NATIONAL INSTRUMENTS 100 Pin 2 meter Cable SH100-100
FREE USA SHIP SAVE $60 NI TBX-68 National Instruments
FREE USA SHIP SAVE $60 National Instruments TBX-68
National Instruments SCXI-1302 Terminal Block ++ NEW ++
National Instruments 182340-01 NB-GPIB-P/TNT Interface
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National Instruments GPIO Interface ASSY 180320-01
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National Instruments PCI-DIO-32HS I/O Device
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NI National Instruments NB-GPIB 181210-01 Card
National Instruments 181485-01 SC-2054 Rev. B
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National Instruments PCI-232/8 Serial Port w/ 68 PinCon
NATIONAL INSTRUMENTS 100 Pin 2 meter Cable SH100-100-F
1794-AENTRXT
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