Most Israeli Jews would probably agree that the heart of Israel is Jerusalem, the heart of Jerusalem is the Old City, and the heart of the Old City is the Jewish Quarter — captured by Israeli troops precisely 45 years ago, an event marked on Jerusalem Day this Sunday.

And yet today’s Jewish Quarter, formed from the ruins and rubble that existed here after the Six Day War, has become a place entirely unlike the country at whose spiritual center it is supposed to exist.

On a recent morning in the Quarter, several contingents of American teenagers were herded across a spotless open square in the direction of the Western Wall. A bearded man sat at a table with a few sets of phylacteries and a banner with a Nike swoosh next to the English words, “Tefillin: Just Do It.”

In a narrow street nearby was the Temple Institute — an organization dedicated to preparing plans for the building the Third Temple — and its gift shop, which does a brisk business in Temple posters, puzzles and balsa wood models. In a different alley, two women with hair covered in severe kerchiefs, their hands resting on stroller handles, conversed in English.

“People dreamed of Jerusalem for 2,000 years. There is a special atmosphere here, and it helps us study,” said Arieh Weintraub, 23, a yeshiva student in a black yarmulke who was taking a break outside the domed Hurva Synagogue on one side of the square.

The unique nature of the Jewish Quarter can be summed up best in two numbers: 3,000, the number of residents, and 2 million, the number of annual tourists.

Trying to navigate the needs of residents and those of visitors “never goes off the agenda,” said Daniel Shukron, secretary of the official body in charge of the Jewish Quarter, the Company for the Reconstruction and Development of the Jewish Quarter in the Old City. (To residents, it is simply “the Company.”)

“It is not easy to find the balance, and no one is happy, which we think means we’re probably doing something right,” Shukron said.

In the other three quarters of the walled Old City, identified with Arab Christians, Armenian Christians, and Muslims, a visitor can sense an authentic and old pulse of life. Families in those quarters have been there, in some cases, for centuries. The Armenians, for example, have had a more or less uninterrupted presence in their quarter dating back 1,600 years.

But life in the Jewish Quarter was ruptured when Jordanian troops captured it in 1948 and expelled all of its residents. Today the reconstructed Jewish Quarter — which is cleaner and more modern than the others, and has a far higher number of tourist sites, excavations and museums, and where many residents are foreign-born — feels less like a Jewish neighborhood than a Jewish theme park.

In the Jewish Quarter there are those gripped by fevered visions of the future, like the people who run the Temple Institute, while others seem to be reenacting a fantasy of the past — Eastern Europe, filtered through the unmistakable prism of Jewish New York. The present, to an observer, can feel artificial and rootless.

The paratroopers who arrived in the Jewish Quarter in 1967 found an area that had been largely in ruin since the Jordanian conquest 19 years before. That provided a nearly blank slate on which the Israeli government could construct the Quarter anew.

The government officially expropriated the land within the Quarter’s boundaries, relocating Arab families who had moved in since the Jews left, and transferred the entire area to the Company for the Reconstruction and Development of the Jewish Quarter, which was to serve both as the contractor and landowner.

The government had contradictory aims — it wanted both to resettle the Quarter with Jews and to create a symbolic landscape and ideological mecca in which archaeology, memorials to the 1948 fighting, and rebuilt institutions from before that war would emphasize the Jews’ historic claim to Jerusalem.

The result, according to a paper published last year by two prominent Israeli geographers, Rehav Rubin and Doron Bar, has been “a new landscape whose connection to the pre-1948 neighborhood is extremely vague.”

Before 1948, the Quarter had been a neighborhood in decline, eclipsed by the modern development in the new city and populated largely by religious Jews whose poverty prevented them from leaving.

The new Jewish Quarter created a revised memory of the old one. Synagogues and yeshivas were rebuilt, the extreme poverty was expunged, and “tourists began to be told highly sentimental stories about the special atmosphere that pervaded the neighborhood,” according to Rubin and Bar.

The Jewish Quarter is home to significant ruins linked to other cultures, but most of those were not developed. Critics have pointed as an example of this policy to the Nea Church, built by the emperor Justinian and one of the city’s great landmarks in Byzantine times, the neglected ruin of which is not open to the public and is barely marked.

What has emerged, the researchers wrote, is “an ideologically driven cultural landscape that links the Israelite kingdom and the Second Temple period with the founding of the modern State of Israel.”

In the midst of this complicated landscape live the 3,000 residents of the Quarter, who veer between praising the otherworldly atmosphere of the neighborhood and complaining bitterly about its inconveniences, chief among them an acute lack of parking.

A recent decision by the Company to more than double parking prices led to calls from some residents for a “revolt” against the Company — a body whose officials are not elected and answer not to Jerusalem’s mayor but to the Housing Ministry, and which is therefore, residents say, opaque and all but unaccountable.

The Company’s secretary, Shukron, says there are plans to alleviate the parking crisis by constructing a new 800-car parking garage accessible via a tunnel under the walls. But the planned start of construction is still distant, and considering the sensitivities of the Old City and especially of the word “tunnel” in a place where tunneling has sparked deadly riots, it is almost certainly more distant still.

In the meantime, though, the Company is constructing an elevator and a moving sidewalk to ease access for visitors to the Western Wall, and is also rebuilding another historic synagogue, Tiferet Yisrael. Like the Hurva, rebuilt and inaugurated in 2010, the synagogue was destroyed by the Arab Legion in 1948, and its reconstruction is part of the restoration of landmarks that existed in the Quarter before it fell. And like the Hurva, its reappearance will do nothing to encourage or ease normal life in the neighborhood.

Nonetheless, many of the Quarter’s residents would rather be nowhere else. “Those who live here feel it is the greatest blessing,” said Aura Wolfe, who moved in 12 years ago.

She defined the Quarter simply as “the center of the world.”

“With all the headaches, like the parking, there’s a feeling of being surrounded by an energy that is unlike any other place on earth,” she said.

In the first years of reconstruction after the Six Day War, the population was drawn from Israel’s mainstream — most residents were religious or secular Zionists, and they included a number of artists and writers and government officials, including the military hero and cabinet minister Yigal Alon.

Bernard Spolsky, a retired linguistics professor, moved into the Jewish Quarter with his wife and two children in 1979.

The streets had yet to be paved, and when they bought an apartment it was a third-floor walk-up located 10 minutes on foot from the parking lot.

“It was worth the inconvenience,” Spolsky said. He remembered wandering the streets in those years, walking down the steps to the Western Wall, enjoying the sense that the landscape was significant — the ancient wall, the Temple Mount to the east.

Beginning in the mid-1970s, however, the population had already begun to shift. The Quarter saw an influx of ultra-Orthodox Jews, many of them English-speakers, willing to pay high real estate prices and suffer the Quarter’s inconveniences in order to be in the historic neighborhood and close to the Western Wall holy site.

Over the years, Spolsky said, the modern Orthodoxy practiced by his family and many of their friends was eclipsed by more extreme forms of practice. A landmark, he said, was a decision in the 1990s by the Quarter’s rabbi that English could not be taught after 4th grade because of a 19th-century prohibition that was, the rabbi had decided, still in effect. The neighborhood became more ultra-Orthodox. Stores catered to tourists, not to residents, and the Company seemed preoccupied with projects like rebuilding the Hurva and not with solving the parking problem.

“They didn’t face the issue: Was it going to be a museum, or a place where people would live?” Spolsky said.

Their children grown, he and his wife finally left the Quarter last year, moving to an airy apartment in the new city with an elevator and ample parking.

Many others have left over the years, and today the Jewish Quarter has an ultra-Orthodox majority, according to the Company. The neighborhood’s focal point, the Western Wall, is run by an ultra-Orthodox organization, the Western Wall Heritage Foundation, that enforces strict gender segregation and modesty rules and restricts religious practice according to its own interpretation of Jewish law. That means that the disputed heart of Israel’s capital, an enclave which Israel had intended to be a symbol of the triumph of Zionism and the state, is now largely in the hands of people who identify with neither.

Mazal Hess was born in the Jewish Quarter in 1926.

Her childhood memories are unsentimental — of large families crowded into small rooms, of dark alleys barely lit by kerosene streetlamps, of rushing through the streets to be home before dark, of the knowledge that they were cut off from the new city by the largely hostile Arab population that surrounded the Quarter.

“The Quarter was poor, and it was frightening at times,” Hess, 85, remembered this week. She spoke from her home on the kibbutz in northern Israel where she moved in 1943.

“Those who could leave left,” she said of those years before 1948. “Those who stayed were, as always, those who had nowhere to go.”

When the Quarter returned to Israeli hands after 1967, she and the members of her extended family went to visit but stayed put in their new homes.

“Those who were born there did not want to go back,” she said.